Free Chinese Remainder Theorem Calculator - Given a set of modulo equations in the form:

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n_{i} portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

This calculator has 1 input.

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n

This calculator has 1 input.

- algorithm
- A process to solve a problem in a set amount of time
- chinese remainder theorem
- ancient theorem that gives the conditions necessary for multiple equations to have a simultaneous integer solution
- coefficient
- a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
- equation
- a statement declaring two mathematical expressions are equal
- gcf
- greatest common factor - largest positive integer dividing a set of integers
- modulus
- the remainder of a division, after one number is divided by another.

a mod b - product
- The answer when two or more values are multiplied together
- remainder
- The portion of a division operation leftover after dividing two integers
- substitution
- a simple way to solve linear equations algebraically and find the solutions of the variables.
- theorem
- A statement provable using logic