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Expression and Perfect Square (
Posted on 20151010
)
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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 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 20151011 09:43:26
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