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Quadratic and Perfect Square Query II (Posted on 2016-05-21)

Determine all possible values of a positive integer N such that:
N² + 72N is a perfect square.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible solution

Comment 1 of 1

72N should have the form 2aN+a^2, with 0<a<36.

This lead to N=a^2/(72-2a)

With integers for N=3,9,24,49,75,128,289,

And the squares are: 15,27,48,77,105,160,323.

Posted by armando on 2016-05-21 10:15:17

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