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Choose To Prime Poser (Posted on 2010-04-18) Difficulty: 3 of 5
Determine all possible values of a positive integer N ≥ 3, such that NC2 1 is a prime power.

Note: NC2 represents N choose 2.

See The Solution Submitted by K Sengupta    
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re(2): No Subject. No real hole in my proof. Comment 4 of 4 |
(In reply to re: No Subject by farcear)

I was thinking of (n-2) and (n+1) which if neither is 1 and they produce a prime power must be each be powers of 3.

The actual factors [1] (.5n-1)(n+1) or [2] (n-2)(.5n+.5) can differ by any value.

This does not change much since exponents grow so fast that
2*p^x+3 = p^y
p^x = 2*p^y - 3

Only have solutions if p=3 anyway (p cannot be 2 due to the +3 or -3)

  Posted by Jer on 2010-04-26 15:42:02

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