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Number Theory divisibility proof

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that for any n [tex]\in[/tex] Z+, the integer (n(n+1)(n+2) + 21) is divisible by 3

    2. Relevant equations

    A previously proved lemma (see below)

    3. The attempt at a solution

    I sort of just need a nudge here. I have a previously proven lemma which states:

    If d|a and d|b, then d|(a+b)

    So armed with this I see that obviously 3|21 and all that remains is to prove n(n+1)(n+2) is divisible by 3. I have tried expanding, which didn't seem to help.
  2. jcsd
  3. Mar 1, 2010 #2
    n(n+1)(n+2) is the product of __ consecutive integers.
  4. Mar 1, 2010 #3
    Wow! staring me in the face. Thanks.
  5. Mar 1, 2010 #4
    Cheers :)
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