Question

Prove that the sum of any consecutive natural number is divisible by 5

Answer 1

• Reading: Theorem: If n is the sum of five consecutive integers, then n is divisible by 5. Conversely, if n is divisible by 5, then n is the sum of five consecutive integers. In particular, this gives n = 5m + 10 = 5(m + 2) and, since m + 2 is an integer, this shows n is divisible by 5.