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 other types of cases by Charlie)

Exactly. y=b^2+1 is simply an obvious substitution. More precisely, y=a^2/(b^2+1), giving many additional possibilities:

a=2n, b=1, x=y=2n^2  
a=5n, b=2, x=5(2n)^2, y=5n^2  
a=10n, b=7, x=2(7n)^2, y=2n^2

etc.

In fact it seems that there are infinitely many solutions for every possible value of b in N.

Edited on September 29, 2014, 3:06 am

Posted by broll on 2014-09-29 02:58:24