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How many positive integers \(n\) less than 100 have a corresponding integer \(m\) divisible by 3 such that the roots of \(x^2-nx+m=0\) are consecutive positive integers?

 Jun 4, 2019
 #1
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As follows:

 

Edit:  I was unnecessarily complicated above:  All I needed to say is n2-1 must be divisible by 12.

 Jun 4, 2019
edited by Alan  Jun 4, 2019

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