Number Theory divisibility proof

  • Thread starter jersiq1
  • Start date
  • #1
jersiq1
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Homework Statement


Prove that for any n [tex]\in[/tex] Z+, the integer (n(n+1)(n+2) + 21) is divisible by 3


Homework Equations



A previously proved lemma (see below)

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.
 

Answers and Replies

  • #2
VeeEight
615
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n(n+1)(n+2) is the product of __ consecutive integers.
 
  • #3
jersiq1
7
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Wow! staring me in the face. Thanks.
 
  • #4
VeeEight
615
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Cheers :)
 

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