Each of X and Y is a positive integer such that each of X+Y and X/Y is a perfect square.

Does there exist an infinite number of pairs (X,Y) satisfying all the given conditions?
Give reasons for your answer.

(In reply to re: Technical solution--but a larger question remains. by Jer)

This is another method:

Let X=Yb^2  (since X/Y=b^2)
Let a^2=Y(b^2+1)  (since X+Y = a^2)
Let Y=(b^2+1)  (an obvious substitution)
Then X+Y = (b^2+1)b^2+b^2+1 = (b^2+1)^2  
And X/Y = Yb^2/Y = b^2  

Posted by broll on 2014-09-28 11:19:03