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Prime and perfect (Posted on 2015-02-27) Difficulty: 2 of 5
Let n and p be positive integers greater than 1, with p being a prime. Show that if n divides p-1 and p divides n^3-1, then 4p-3 is a perfect square.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Solution - may not be complete | Comment 2 of 3 |
(In reply to Solution - may not be complete by Jer)

Jer, I believe your proof is complete.

Under the given conditions, p is always of the form n^2+n+1, so is potentially prime. The fact that some numbers of that form may not be prime does not affect the fact that the stipulation 4p-3 is a perfect square is true of those that are.

See also the very first comment under Sloane A002383


  Posted by broll on 2015-02-28 22:03:17
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