Question

Prove that congurence relation on integers is an equivalence relation

Answer 1

Answer:

CONGRUENCE MODULO N IS AN EQUIVALENCE RELATION: it is reflexive, symmetric and transitive. ... (c) If a ≡ b mod N and b ≡ c mod N , then a ≡ c mod N (congruence is transitive). (2) Prove that every a ∈ Z is congruent mod N to some r ∈ Z such that 0 ≤ r<N.