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April 8th, 2014, 02:47 AM   #1
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Prove or disprove

Prove or disprove the claim that for any positive integer m there is a positive integer n such that mn + 1 is a perfect square

My attempt:
After trying out a few concrete examples I noticed that n has to be m + 2

So here's my proof
Let n = m + 2
so mn + 1 = m(m + 2) + 1 = m^2 + 2m + 1 = (m + 1)^2

So for every m there exists an n such that n = m + 2 that makes mn + 1 a perfect square.

Is this proof acceptable? Is there a better way? thanks
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April 8th, 2014, 03:04 AM   #2
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Your proof is correct.
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