Congruence modulo calculator with steps. The calculator accepts numbers of up to 10000 .

Congruence modulo calculator with steps. Conclusion: The concept of inverse modulo is worth considering as it aids in determining the solutions to the linear system of congruences. Use this Congruence Modulo N Online Calculator for your discrete math mod problems! This modulo congruence calculator makes it easy to verify congruent modulo calculations. [1] In the standard notation of modular arithmetic this congruence is written as which is the shorthand way of writing the statement that m divides (evenly) the quantity ax − 1, or, put another way Example \ (\PageIndex {1}\): Suppose \ (n= 5, \) then the possible remainders are \ ( 0,1, 2, 3,\) and \ (4,\) when we divide any integer by \ (5\). Mar 6, 2021 — Solving Systems of Linear Congruences 2. Prove that 23 ≡ (mod 4) Oct 12, 2024 · A: Congruence can be used to solve problems in areas such as timekeeping, calendar systems, and cryptography. An instance of this: "What an extraordinary congruence of genius and era" (Rita Rack). 8K Dislike Modulo inverse calculator with steps using euclid's algorithm Tool to compute the modular inverse of a number. This tool also comes with detailed learn sections, step-by-step solutions, & practice problems! Free Congruence Modulo n Calculator - Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n). 1. 2 Simple Method. Jul 5, 2025 · Solve modular arithmetic problems online with steps. Use our mod calculator or calculate manually. congruence (with something) The results show quite good congruence with recent studies. Free Modulo Congruence with Variables Calculator - find whether two numbers are congruent to same module step by step This modulo congruence calculator makes it easy to verify congruent modulo calculations. An example is also provided to explain this th The CRT is used solve systems of congruences of the form $\rm x\equiv a_i\bmod m_ {\,i}$ for distinct moduli $\rm m_ {\,i}$; in our situation, there is only one variable and only one moduli, but different linear congruences, so this is not the sort of problem where CRT applies. The state of being congruent. Aug 27, 2024 · Congruence Calculator Calculate In the world of math, congruence calculation is a powerful tool. The meaning of CONGRUENCE is the quality or state of agreeing, coinciding, or being congruent. Brian was born on March 27, 2001. Sep 9, 2017 · Step by step instructions to find modular inverses. To solve mod , enter the value for , and the modulus . com: fast, accurate, and easy. In this section, we will be discussing linear congruences of one variable and their solutions. As you can see, the time values wrap after reaching 12 and 9 + 4 = 13 is computed as remainder of 13 when divided by 12. This theorem (Quadratic Reciprocity, in the next chapter) will come from our trying to find the solution to a useful general problem, which I like to think of as the last piece of translating high school algebra to the modular world. Modulo Calculator for Power Mod Power mod calculations have endless applications in cryptography. Modular arithmetic is sometimes called clock arithmetic, since analog Use this Congruence Modulo N Online Calculator for your discrete math mod problems! This modulo congruence calculator makes it easy to verify congruent modulo calculations. Instead, you are working with a $2\times2$ linear system over a given modulus, $9 One can ask very similar questions (and many more) about the integers modulo . Kindly consider subscribing to this channel for more tricks and techniques. This calculator uses the bigInt library implementation of the fast modular exponentiation algorithm based on the binary method. Instantly calculate remainders with Vedantu’s Modulo Calculator. A statement that two quantities are congruent. The Chinese Remainder Theorem Calculator is a theorem that gives a unique solution to a system of congruences with pairwise coprime moduli. And this is why we have developed this inverse modulo calculator with steps to calculate the exact inverse in terms of modulus for any integer number. Get the solution of modular equations using our Chinese Remainder Theorem Calculator. In other words, it’s like solving the equation x * a ≡ 1 (mod m), where x is the unknown and a and m are known integers. It is often used in informatics and cryptography. The best method to calculate the modulus (the remainder) of a number using a normal scientific calculator Casio (557 or 991). Extended Euclidean Algorithm, Euclid's Algorithm, Modular multiplicative inverse 1. Step 3: Convert the result back to hexadecimal if needed. In this case, we can multiply both sides of the equation by a−1 a 1 to isolate x x: x ≡ a−1b (mod m) x ≡ a 1 b (mod m) The modular inverse a−1 a 1 can be found using the extended Euclidean algorithm 4. The PowerMod Calculator, or Modular Exponentiation Calculator, calculates online a^b mod n step-by-step Use this Congruence Modulo N Online Calculator for your discrete math mod problems! This modulo congruence calculator makes it easy to verify congruent modulo calculations. The concept is widely used in Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. Use the calculator below to get a step-by-step calculation of the Chinese Remainder Theory. For each mi m i, calculate Mi = M mi M i = M m i. Jun 16, 2025 · This Web application can solve equations of the form a⁢x² + b⁢x + c ≡ 0 (mod n) where the integer unknown x is in the range 0 ≤ x < n. The number is called the modulus, and the statement is treated as congruent to the modulo. Aug 29, 2024 · Introduction Continuing with the series of posts on number theory and cryptograpy, let us take a look at the Chinese Remainder Theorem. The modulo calculator returns the rest of the integer division. First iss $$ a^p \equiv a \mod p $$ If $ a $ is divisible by $ p $, then both sides of the congruence are 0 modulo $ p $, making the statement trivially true. n So we will focus on congruences, which are simply equations modulo n (see Definition 4. Recall the division algorithm: given a ∈ and n ∈ there exist unique q, r ∈ such that Master modular arithmetic with our power mod calculator, perfect for calculations with exponents. 7 and 11 3. What day of the week was this, given that June 1, 2014 was a Sunday? While writing up an answer for this specific case, I learned about the Doomsday method and Zeller's congruence and wrote up some notes showing how to use those methods to solve this problem as well. Our Chinese 3 Congruences and Congruence Equations A great many problems in number theory rely only on remainders when dividing by an integer. the quality of being similar to or in agreement with something: 2. Get the free "Modulo" widget for your website, blog, Wordpress, Blogger, or iGoogle. 6. So when it is ax + b (mod m), Find of a and m Figure out if gcd divides evenly into b, if yes move on or else call it a day Somehow figure out the smallest number that can Solves for linear congruence modulo statements in the form ax = b mod c Get the tablet and products I use for math here: https://www. It is widely used in number theory, cryptography, computer science, and various algorithms. Just enter the numbers you would like and press "Calculate" . amazon. Modular Exponentiation (or power modulo) is the result of the calculus a^b mod n. Aug 27, 2017 · About This is a modular arithmetic calculator, inspired by wanting to make it possible to experiment with the mathematics behind cryptography. Learn how to use it with applications. Get instant results with primary and secondary inverse modulo calculations. the quality of being similar…. You may also enter the math expression containing other integers and the following modular arithmetic operations: + addition modulo p - subtraction modulo p * multiplication modulo p / division modulo p (available for all numbers if Explore our online Inverse Modulo Calculator tool, designed to make complex calculations easy. According to the theorem: $$ 5^ {2-1} \equiv 1 \mod 2 $$ $$ 5 \equiv 1 The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context. Get the free "congruent" widget for your website, blog, Wordpress, Blogger, or iGoogle. In this case, we will have only a finite solution in the form of \ (x \equiv (mod \,m)\). In my specific case the congruence is of the form: x^3 Although there are existing methods for solving linear congruence ax ≡ b (mod n), finding solutions still remain difficult especially when the modulus n is large. Jul 23, 2025 · Given three positive integers A, B, and N, which represent a linear congruence of the form AX=B (mod N), the task is to print all possible values of X (mod N) i. So, 62 2 7 4 2 4 2 0. Definition of congruence noun from the Oxford Advanced Learner's Dictionary. The Chinese Remainder Theorem helps to solve congruence equation systems in modular arithmetic. e. They solve math problems more efficiently and accurately now. Learn how to solve for the variable. Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. What is Modulo? Free Modular Exponentiation and Successive Squaring Calculator - Solves x n mod p using the following methods: * Modular Exponentiation * Successive Squaring This calculator has 1 input. There are several algorithms for finding all linear congruence solutions, this calculator uses an algorithm for solving linear Diophantine equations in two variables. What a bummer. 4x is congruent to 8 (mod 5)2. The modulus is another name for the remainder after division. 2. 2) Solving 23 power 3 mod 30 with cl For example to calculate with the expression \ (12^5+89\times (15^6-13^7)\) whilst working modulo \ (8\), instead of expanding the expression to find it equals \ (-4570603556\) and then trying to calculate which number it is congruence to modulo 8, we can replace different parts of the expression and simplify as we go along. Two angles are said to be congruent if they are of equal measure. Congruence can be applied to line segments, angles, and figures. Free Congruence Modulo n Calculator - Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n). So, by the definition of congruence, we have 62 ≡ 0 (mod 4). 2x = 7 (mod 17): Free Linear Congruence Calculator - Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists Step 2: Calculate the Modulus Factors. Is $10 T 1 ?$ Is $1 May 14, 2025 · Fraction Calculator: To simplify, add, subtract, multiply, or divide fractions Final Thoughts The Remainder Calculator makes it easy to handle division-based problems and explore modular arithmetic. Baby-step giant-step algorithm Given a cyclic group G of order 'm', a generator 'a' of the group, and a group element 'b', the problem is to find an integer 'k' such that a k ≡ b (m o d m) ak ≡ b (mod m) Expand/collapse global hierarchy Home Campus Bookshelves Mount Royal University Higher Arithmetic 3: Modular Arithmetic 3. To calculate, enter the integers a and m, then click the 'Calculate' button. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms. Discover the free modulo inverse calculator at NiceCalculators. Network Security: Modular Exponentiation (Part 1)Topics discussed:1) Explanation of modular exponentiation with examples. For each Mi M i, compute the modular inverse M−1i M i 1 modulo mi m i. You can type numbers or numerical expressions on the input boxes at the left. [Step-by-Step] The congruence modulo 3 relation, T, is defined from Z to Z as follows: For all integers m and n, m T n => 3 \mid (m-n). calculate mod with only one step 0 A linear congruence equation is equivalent to a linear equation where all coefficients and all variables are from the Set of Integers (Z). Dec 28, 2022 · @markiedoesmath Modulo Operator Examples #Shorts #math #maths #mathematics #computerscience 3. The modular multiplicative inverse of an integer N modulo m is an integer n such as the inverse of N modulo m equals n. How to solve a linear congruence (General Case) Input: A congruence equation ax b (mod n) featuring Pretty lost on how to do this stuff! Professor kind of rushed through it and had an important call. Mathematically, this can be expressed as b = c (mod m) Generally, a linear congruence is a problem of finding […] Chinese Remainder Theorem Calculator: A Guide to Solving Linear Congruences The Chinese Remainder Theorem (CRT) is a powerful mathematical tool that helps solve systems of linear congruences. This problem could be . Step 4: Combine Solutions. Solve modular inverses with step-by-step solutions! Tool to compute modular power. Numbers are congruent if they have a property that the difference between them is integrally divisible by a number (an integer). Feb 1, 2021 · Modular arithmetic, sometimes called clock arithmetic, involves divisibility and congruence, and examines the remainder. See relevant content for chinese-remainder-calculator. This tool also comes with detailed learn sections, step-by-step solutions, & practice problems! Jul 5, 2025 · Solve modular arithmetic problems online with steps. . Online Chinese Remainder Theorem Calculator Solve a system of congruences using chinese remainder theorem. Mathematics a. Apr 9, 2022 · Find question and solution here; The steps are clearout of interest i decided to use the other equation; may i say that i underestimated the euclidean algorithm :biggrin: in trying to find the inverse of modulo arithmeticof course we have the online calculator. (1) If b-c is not integrally divisible by m, then it is said that "b is not In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. In particular, it can find modular square roots by setting a = -1, b = 0, c = number whose root we want to find and n = modulus. Our system of . Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. It is often referred to as "clock arithmetic. Let one solution to the original equation be x_0<m/d. The calculator accepts numbers of up to 10000 Step 2: Perform the modulo operation in decimal. 6 2 for some integer . Thanks to addition and multiplication properties, modular arithmetic supports familiar algebraic manipulations such as adding and multiplying together ≡ (mod m) equations. Proof. We'll start by looking at the basics of modulo arithmetic. Try now! Jul 23, 2025 · Time complexity of this approach is O (m) An efficient approach is to use baby-step, giant-step algorithm by using meet in the middle trick. This tool also comes with detailed learn sections, step-by-step solutions, & practice problems! Congruence modulo calculator with steps If you think back to doing division with whole numbers, you may remember finding the whole number result and the remainder after division. In this section, you’ll learn about modulo, its basic operation, and its uses in real life. Now, we look to include variables in equivalence relations and solve for those variables. Euclidean Algorithm Extended To solve a linear congruence ax ≡ b (mod N), you can multiply by the inverse of a if gcd(a,N) = 1; otherwise, more care is needed, and there will either be no solutions or several (exactly gcd(a,N) total) solutions for x mod N. Then finally, we subtract the answer in the second step from the Dividend (10) to get the answer. Find inverse modulo, power mod, and congruence solutions. The modulo calculator helps to perform modulo operation between two numbers step by step. Sep 3, 2022 · This video discusses how to solve a system of quadratic congruences for the variable x. Systems of Congruences Solve a single congruence equation: solve 5x =2 (mod 3) Solve systems of congruences: solve 2x = 10 (mod 12), 3x = 9 (mod 12) Check if values are equivalent under a given modulus: 17 = 7 mod 10 Solve a congruence involving variables in the modulus: solve 22 = 10 mod n Solve systems with each equation under a different Linear Congruence Calculator: Free Linear Congruence Calculator - Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists The Chinese remainder theorem calculator is here to find the solution to a set of remainder equations (also called congruences). 4x is congruent to 2 (mod 5)3. How to use congruence in a sentence. Step 3: Compute the Inverses. Is \ (6 \, \equiv Jul 12, 2025 · Modular arithmetic is a system of arithmetic for numbers where numbers "wrap around" after reaching a certain value, called the modulus. Let 2 be an integer. Unless you only want to use this calculator for the basic Euclidean Algorithm. (formal) agreement with something; the state of being similar to something and not in conflict with it synonym compatibility. Named after its discovery in ancient Chinese mathematics, this theorem provides a systematic way to find a unique solution when we have several congruence equations with coprime moduli. Here's how to calculate a b m o d m ab mod m: You need to use the method of exponentiation by squaring for efficiency. a. Agreement, harmony, conformity, or correspondence. Modular Dec 10, 2008 — A linear congruence is the problem of finding an integer x satisfying ax ≡ b (mod m) for specified integers a, b, and m. , (b-c)/m is an integer), then b and c are said to be "congruent modulo m. Example Let’s consider a case where the modulus is the prime number $ p=2 $, and $ a = 5 $, which is not divisible by $ p $. With step-by-step solutions, multiple calculation options, and visual aids, it’s a helpful tool whether you're solving homework or developing Jan 15, 2018 · What's wrong with changing your if statement to check both congruences at the same time? You would need to change your parameter list to include the new congruence, of course. If we are given a set of simultaneous linear congruences, with one (or more) of them in the more general form \ (ax\equiv b\text { mod } (n_i)\), then we will first need to use the earlier algorithm to solve this congruence, expressing its general solution as a congruence class modulo some divisor of \ (n_i\); it will then be possible to apply Calculators that use this calculator Bézout coefficients Egyptian fraction expansion Egyptian numbers Hill cipher Inverse Modulo Calculator Linear congruence solver Linear Diophantine equations Modular inverse of a matrix Rhind papyrus and fraction expansion algorithms Jan 17, 2010 · So you first converted between bases, but now there's variables in the way. Modular Arithmetic Calculation Using Calculator. Learn more. Modular multiplicative inverse in case you are interested in calculating the modular multiplicative inverse of a number modulo n using the Extended Euclidean Algorithm Input Algorithm Choose which algorithm you would like to use. What I get is we can't treat this like normal algebra. One of the neat As we mentioned in the introduction, the theory of congruences was developed by Gauss at the beginning of the nineteenth century. e in the range [0, N-1] that satisfies this equation. Use CompSciLib for Discrete Math (Number Theory - Euclid's Algorithm) practice problems, learning material, and calculators with step-by-step solutions! Apr 23, 2018 · Learn how to solve basic linear congruences for your number theory class. n. For example, in a 12-hour clock, the time 10:00 is congruent to 2:00 modulo 12. Learn how it works with addition, subtraction, multiplication, and division using rules. May 24, 2024 · What is modular arithmetic with examples. There is a quicker way for large values of C but for such a small value as 26 that would be overkill. In Lithuania, it's changing how people and teachers work with numbers. 11 and 12 2. The term modular arithmetic is used to refer to the operations of addition and multiplication of congruence classes in the integers modulo n. Aug 1, 2025 · Modulo calculator finds a mod b, the remainder when a is divided by b. HOW TO USE THE CALCULATOR TO Using the Chinese remainder theorem, the problem is reduced to the case of a prime power p n: 🔍 In This Video:- Background on Linear Congruence: Discover the foundational principles of linear congruence equations and why they're a cornerstone in modu 6 days ago · A linear congruence equation ax=b (mod m) (1) is solvable iff the congruence b=0 (mod d) (2) with d=GCD (a,m) is the greatest common divisor is solvable. Because congruences are analogous to equations, it is natural to ask about solutions of linear equations. A Modular Arithmetic Calculator is a tool used to perform calculations involving modular arithmetic. This tool also comes with detailed learn sections, step-by-step solutions, & practice problems! Tool to compute congruences with the chinese remainder theorem. The question is 4x=3 for modulus 5 m Sep 19, 2020 · This video is about a theorem for the solution of the system of congruences in two variables and its solution. It makes complex problems easier to solve. b. 3 that working modulo a positive integer forms a special kind of equivalence relation known as a congruence relation. It shows you the solution, graph, detailed steps and explanations for each problem. See how using the TI-84 smore The Modular Inverse Method If the coefficient a a has a multiplicative inverse modulo m m —that is, if gcd(a,m) = 1 gcd (a, m) = 1 —then there exists an inverse a−1 a 1 modulo m m. 1: Modulo Operation Expand/collapse global location While you still can simply enter an integer number to calculate its remainder of Euclidean division by a given modulus, this modulo calculator can do much more. mod 4 . com/shop/mathcele This inverse modulo calculator calculates the modular multiplicative inverse of a given integer a modulo m. That mathematics is the mathematics of modular arithmetic. Get answers, formulas, and easy examples to master modulo in maths fast! Jun 24, 2025 · What’s an Inverse Modulo Calculator? An inverse modulo calculator is a handy tool that finds the multiplicative inverse of a number relative to a given modulus. The question is 2x^2+7x+=04 for modulus of any prime number. Then click on the calculate button. 3). That is the task of solving quadratic congruences, the modular equivalent to the well-known quadratic equations. References: 3. Find more Mathematics widgets in Wolfram|Alpha. 4x i Inverse Modulo Calculator Calculator for the modular multiplicative inverse This function calculates the multiplicative inverse x from an integer a and modulo m. The same article describes a version of this algorithm, which processes the binary digits from most significant to less significant one (from left to right). 1. Solving Congruences We know from Section 4. Tool to compute any modulo operation. Simplify complex math effortlessly. Il y a plusieurs algorithmes pour trouver toutes les solutions de la congruence linéaire, ce calculateur utilise un algorithme pour résoudre les équation diophantiennes à deux variables. andyborne. Tool/solver to resolve a modular equation. For example, 4 ≡ 16 mod 6 since 6 ∣ 16 4. Modular arithmetic is a system of arithmetic for integers, where numbers “wrap around” after reaching a certain value, called the modulus. Finally, the solution x x to the system of congruences is given by: Apr 26, 2024 · What is the Chinese remainder theorem with the statement, formula, proof, and examples. The logical operator XOR sums 2 bits, modulo 2. The modulo operation returns the remainder in division of 2 positive or negative numbers or decimals. Congruence Modulo n Calculator: Free Congruence Modulo n Calculator - Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n). " The number m is called the modulus, and the statement "b is congruent to c (modulo m)" is written mathematically as b=c (mod m). a = b (mod c Sep 2, 2022 · Linear Congruence with Prime ModulusThis video discusses how to solve a system of linear congruences for the variable x. CONGRUENCE definition: 1. For example 25x = 15 (mod 29) may be rewritten as 25x1 = 15 - 29x2. It mainly uses remainders to get the value after wrap around. Oct 6, 2020 — Modular Equation Solver. I tried reading about it but it isn't clicking with me to be honest. Thanks for watching this simple calculator tricks. The linear congruence equation ax = b (mod n) may be rewritten as ax1 = b - nx2 where x1, x2 -E- Z. Modulo is the name of the calculation of the remainder in the Euclidean division. Thus, this paper aimed to develop a linear congruence solver that will provide step by 6 days ago · If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i. Any two line segments are said to be congruent if they are equal in length. Rather, this is linear algebra. Proposition 5. but i always like Find more at https://www. We will solve 1. Comprehensive modular arithmetic calculator with operations, Chinese Remainder Theorem, congruences, and interactive examples. This calculator has 3 inputs. com/math See how to solve Linear Congruences using modular arithmetic. A modular equation is a mathematical expression presented in the form of a congruence with at least one unknown variable. We are going to solve Equations involving modulo arithmetic. For example, 17 mod 5 = 2, since if we divide 17 by 5, we get 3 with remainder 2. Here’s a step 23 ≡ 5 6 is even. Khan Academy Khan Academy In this video, we are going to look at the topic Modular Arithmetic. This inverse element, when multiplied by the original number, equals 1 when divided by the modulus. An online Systems of linear Equations Calculator for solving simultanous equations step by step. 3 and 7 Online PowerMod Calculator. com A linear congruence is similar to a linear equation, solving linear congruence means finding all integer \ (x\) that makes, \ (ax \equiv b (mod \,m)\) true. We use this in many places in every day life, the most obvious being clock arithmetic where we wrap around the clock: 4 hours on from 11 o'clock is not 15 o'clock but 3 o'clock. Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (7). To exemplify this, consider the following similar ideas: Apr 13, 2011 · Is there an algorithm that can solve a non-linear congruence in modular arithmetic? I read that such a problem is classified as NP-complete. We will learn how to find the (mod x) and so on. If we can construct one solution to the linear congruence \ (ax\equiv b\) (mod \ (n\)), we can construct all of them, and we know exactly how many there are. Congruence calculation with method explanation and examples. Si c'est un multiples, alors le nombre de solutions modulo m est égal au PGCD résultant. Modulo Method To find 10 mod 7 using the Modulo Method, we first divide the Dividend (10) by the Divisor (7). Prereseqisites Modular arithmetic, especially modular inverses The Extended Euclidean Algorithm The Chinese Remainder Theorem The Chinese Remainder Theorem (CRT) provides a solution to a system of simultaneous congruences with different moduli. We would like to show you a description here but the site won’t allow us. In mineralogy and chemistry, the term congruent (or incongruent) may refer to: In geometry, congruent means identical in shape and size. Try it today! Oct 24, 2019 · People use modular arithmetic all the time, especially with anything involving remainders, time and calendar schedules. 3. This will help us understand remainders and divisibility better. This tool calculates the modulo of two integers. Find the congruent values and get accurate results in a few seconds. sett svdz egixj kcaxu zdik mscjc lfy wpescj dtbyu jrpl