Question

Prove that the product of any three consecutive positive integers must be divisible by 3.​

Answer 1

If n = 3k + 2, then n + 1 = 3k + 2 + 1 = 3k + 3 = 3(k + 1) which is again divisible by 3. So we can say that one of the numbers among (n, n + 1 and n + 2) is always divisible by 3. Therefore the product of numbers n(n+1)(n+2) is always divisible by 3.

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