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
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
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