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Find all positive integers m such that m^2 + 2015 is a perfect square.

 Nov 24, 2019
 #1
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48^2  -  2015 = 289

 

sqrt(289) = 17, so:

 

M = 17. 17^2 + 2015 = 2,304 - which is a perfect square of 48^2 =2,304

 Nov 24, 2019
 #2
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m = 17  and m = 71 and m =199 and m =1,007

 

So, you have 4 values that give perfect squares.

 

P. S. I only checked numbers up to 1,000,000.

 Nov 24, 2019

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