Let n and p be positive integers greater than 1, with p being a prime. Show that if n divides p1 and p divides n^31, then 4p3 is a perfect square.
(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 4p3 is a perfect square is true of those that are.
See also the very first comment under Sloane A002383

Posted by broll
on 20150228 22:03:17 