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Perfect square.

Source: Greece National Olympiad 2002 , Seniors , Problem 4.

November 18, 2005
number theory proposednumber theory

Problem Statement

(a) Positive integers p,q,r,ap,q,r,a satisfy pq=ra2pq=ra^2, where rr is prime and p,qp,q are relatively prime. Prove that one of the numbers p,qp,q is a perfect square. (b) Examine if there exists a prime pp such that p(2p+1āˆ’1)p(2^{p+1}-1) is a perfect square.
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