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Expression and Perfect Square (Posted on 2015-10-10) Difficulty: 3 of 5
Each of X, Y and Z is a nonzero integer such that:

Z = X + Y/X – 1/Y is an integer.

Is Z always a perfect square?
Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Thoughts | Comment 1 of 2
it's easy enough to show x=z=y^2 is a solution.  The trick is to show there are no other solutions. 

A possible line of attack is to solve for x. The resulting quadratic's discriminant is a square if z=y^2.  But again, how to show that's the only way?



  Posted by Jer on 2015-10-11 09:43:26
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