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Proving divisibility (Posted on 2017-01-08) Difficulty: 2 of 5
Given two integers n (n>1) and an odd prime p. Without loss of generality let p=2k-1.

Prove that if C(n,2) - C(k,2) is divisible by p, it must be divisible also by p2.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts Prime indeed. | Comment 1 of 2
I guessed that p needed to be odd but not prime for this to work.  I was able to prove that thought wrong:

n=8, k=5, p=9 (not prime)
C(8,2)-C(5,2)=18 which is divisible by 9 but not 9^2
(It is divisible by 3 and 3^2 so the given problem may have a more general proof.)

  Posted by Jer on 2017-01-08 16:13:31
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