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Modular Equation Solver

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.

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Modular Equation Solver -

Tag(s) : Arithmetics

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# Modular Equation Solver

## 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:

### What is a modular equation? (Definition)

A modular equation is an equation (or a system of equation, 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, 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 per line or separate them with operator &&.

### How to write the congruence symbol ≡?

It is not necessary to write it (congruent) so that dCode can solve the equations, the equal sign = is enough.

## Source code

dCode retains ownership of the online "Modular Equation Solver" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Modular Equation Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "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.) and all data download, script, copy-paste, or API access for "Modular Equation Solver" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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