Why always square?

Number Theory Level 3

Find the sum of all positive integers n n for which n 2 + 96 n^2+96 is a perfect square.


The answer is 40.

Lakshya Singh by Lakshya Singh , 19, India

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1 solution

Lakshya Singh
May 24, 2016

Let (n^2)+96= x^2

=x^2-n^2=96

=(x+n)*(x-n)= 96

Listing all factors of 96=1,2,3,4,6,8,12,16,24,32,48,96

solving the above we find 4 solutions for x and n:

  • x=10 and n=2
  • x=11 and n=5
  • x=14 and n=10
  • x=25 and n=23

so adding all values of n =2+5+10+23= 40

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Did the exact same

Aditya Kumar - 5 years ago

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It is the simplest way. Do not know any other way to do this problem.

Lakshya Singh - 5 years ago

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