perplexus.info :: Just Math : Expression and Perfect Square

Expression and Perfect Square (Posted on 2015-10-10)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Thoughts

| Comment 1 of 3

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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