Thread: Short Inductive Proof

Need a little help on this proof...last one on the assignment can't figure it out.

For any integer k, show that k(k+1)(k+2) is congruent to 0 (mod 6).

Tried to prove this was divisible by 6 a few different ways but couldnt manage it. I believe this is related to induction. Thanks.

Originally Posted by gdiamond29

Need a little help on this proof...last one on the assignment can't figure it out.

For any integer k, show that k(k+1)(k+2) is congruent to 0 (mod 6).

Tried to prove this was divisible by 6 a few different ways but couldnt manage it. I believe this is related to induction. Thanks.

You don't even need induction here: if you have three consecutive natural numbers, then at least one is even and EXACTLY one is a multiple of 3...and that's all.

Tonio