Congruence refers to congruence theorem and is an important concept in number theory. Given a positive integer m, if two integers A and B satisfy that a-b can be divisible by M, that is, (a-b)/m gets an integer, then the integers A and B are said to be congruent with the module M, and recorded as a≡b(mod m). The congruence of module m is the equivalence relation of integers.

Mathematically, when two integers are divided by the same integer, if they get the same remainder, they are congruent (English: modular operation, German: Kongruenz). Congruence theory is often used in number theory. The first person to quote the concept and symbol of congruence was the German mathematician Gauss. Congruence theory is an important part of elementary number theory and one of the important tools to study integer problems. It is very simple to demonstrate some divisibility problems with congruence. Congruence is an important part of mathematics competition.

1, congruence symbol

Two integers a and b are said to be congruent with module m, or a is congruent with module b if the remainder obtained by dividing them by m is equal.

Note: a≡b (mod m),

Pronounced as: the module M of A and B is congruent, or read as the module M of B, such as 26≡2(mod 12).

2. Definition

Let m be a positive integer greater than 1, and A and B are integers. If m|(a-b), a and b are said to be congruent with respect to module m, which is expressed as a≡b(mod m) and read as a and b are congruent with respect to module m. ..

Obviously, there are the following facts.

(1) If a≡0(mod m), then m | a；;

(2)a≡b(mod m) is equivalent to dividing a and b by m respectively, and the remainder is the same.