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 Technical solution--but a larger question remains.
Of course there are.
Take any perfect square that is a multiple of 5.
Make x be 4/5 and y be 1/5 of that square.
x/y will be 4.
Take any perfect square that is a multiple of (p+1) where p is a square
x = p/(p+1) and y=1/(p+1) of that square
There are other ratios that will also work for certain square.
Posted by Jer
on 2014-09-28 10:04:46