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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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Required integer values for N are =3,9,24,49,75,128,289,
And the corresponding squares are: 15,27,48,77,105,160,323.
Explanation:
72N should have the form 2aN+a^2, with 0<a<36.
This leads to N=a^2/(72-2a)
This gives:
N N^2+72N 3 15^2 9 27^2 24 48^2 49 77^2 75 105^2 128 160^2 289 323^2

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	Possible solution	armando	2016-05-21 10:15:17

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