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

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In the particular case of **a single unknown** with several equations with **several modulos**, there is the Chinese remainder theorem:

⮞ Go to: Chinese Remainder

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.

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.

Enter one equation/congruence per line or separate them with operator `&&`.

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.

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Cite as source (bibliography):

*Modular Equation Solver* on dCode.fr [online website], retrieved on 2023-10-01,

modular,modulo,mod,equation,congruence,congruent,modulus,equality,calculator

https://www.dcode.fr/modular-equation-solver

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