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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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Some Thoughts re(2): Technical solution--but a larger question remains. | Comment 3 of 6 |
(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
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