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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 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

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Modular Equation Solver on dCode.fr [online website], retrieved on 2023-10-01, https://www.dcode.fr/modular-equation-solver

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