Let n ≥ 1 be an integer. Show that in any set of n consecutive integers, there is exactly one that is divisible by n. Hint: Express the smallest integer in the set as q ⋅n+r, where q, r are integers satisfying 0 ≤ r ≤ n−1.

Question : Let n ≥ 1 be an integer. Show that in any set of n consecutive integers, there is exactly one that is divisible by n.
Hint: Express the smallest integer in the set as q ⋅n+r, where q, r are integers satisfying 0 ≤ r ≤ n−1.

Answer: