Tool/solver to resolve a modular equation. A modular equation is a mathematical expression presented in the form of a congruence with at least one unknown variable.
Modular Equation Solver - dCode
Tag(s) : Arithmetics
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Modular Equation Solver
Modular Equation Calculator
Solve Equations with Several Modulos
In the particular case of a single unknown with several equations with several modulos, there is the Chinese remainder theorem:
Answers to Questions (FAQ)
What is a modular congruence? (Definition)
A modular congruence is a kind of equation (or a system of congruence, with at least one unknown variable) valid according to a linear congruence (modulo/modulus). With modulo, rather than talking about equality, it is customary to speak of congruence.
For several modulus equations system (non linear), this is a different calculation that can be solved with the calculator tool solving the Chinese remainders problem available on dCode.
How to solve a modular equation?
Enter the equation/congruence, the variables and the value of the modulo. The value of the modulo is global and applies to all equations.
Example: $$ x+12 \equiv 3 \mod 5 \Rightarrow x = 1 $$
The modular equation solver can not work with inequalities, only the equal sign is accepted to solve the equations.
How to solve multiple equations?
Enter one equation/congruence per line or separate them with operator &&.
How to write the congruence symbol ≡?
Copy this symbol: ≡ (Unicode U+2261)
In LaTeX, write: \equiv
On dCode, it is not necessary to write it ≡ (congruent) to solve the equations, the equal sign = is enough.
Source code
dCode retains ownership of the "Modular Equation Solver" source code. Any algorithm for the "Modular Equation Solver" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "Modular Equation Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) or any database download or API access for "Modular Equation Solver" or any other element are not public (except explicit open source licence like Creative Commons). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Modular Equation Solver" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source.
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Modular Equation Solver on dCode.fr [online website], retrieved on 2025-04-15,
