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Square Result Rumination (Posted on 2014-09-28) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Solution Technical solution--but a larger question remains. | Comment 1 of 6
Take any even perfect square. Make x and y each be 1/2 that square. As x and y are equal, x/y will be 1, a perfect square. There are infinitely many of these.

But are there infinitely many where x is not equal to y?

  Posted by Charlie on 2014-09-28 09:04:20
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