Modulo M

Modulo M. A = 100, b = 13, m = 107 output: 10+20 = 30 % 3 = 0 input:

Theorem let m ≥ 2 be an integer and a a number in the range 1 ≤ a ≤ m − 1 (i.e. From the euclidean division algorithm and bézout's identity, we have the following result about the existence of multiplicative inverses in modular arithmetic: A and b have the same remainder when divided by m.

1) reflexive only 2) transitive only 3) symmetric only 4) an equivalence relation.

Each power b i is coprime to m, and there are φ ( m) integers coprime to m. Sometimes, we are only interested in what the remainder is when we divide by. A = 100, b = 13, m = 107 output: It follows that each of the powers are distinct modulo m, and thus each.