p, q and r are three positive integers satisfying 1/p + 1/q = 1/r, such that there is no integer ≥ 2 dividing p, q and r simultaneously. However, p, q and r are not necessarily pairwise coprime .

Prove that (p+q) is a perfect square.

(In reply to p+q IS a square by C W Gardner)

I read your consideration and is interesting , but is only a particular solution. There are solution to the problem but the numer are not like n*(n-1) ; n and (n-1) 

Example!

p=5*7 ; q=7*2 ; r=2*5

1/35+1/14=1/10 and (35,14,10)=1

Posted by Chesca Ciprian on 2007-09-28 14:59:17