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Math Help - Short Inductive Proof

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by gdiamond29 View Post
    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
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