number theory again

Number Theory Level 3

Find the number of positive integers n n , for which

2 n + 1 2 n + 15918 7 n 2^n+12^n+159187^n

is a perfect square.


The answer is 1.

Michael Wu by Michael Wu , 23, Indonesia

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1 solution

159187 is very close with 40 0 2 400^{2} but closer with 39 9 2 399^{2} = 159201.
The difference between 159201and 159187 is 14. Seems that n should be 1

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Same guess!!!! ..... But I think solution should have been more rigorous....😉

Abhinav Raichur - 6 years, 11 months ago

but, are you sure that is the unique solution?

Iancarlo Espinosa - 6 years, 11 months ago

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Yes, I guess since 2, 12, 159187 and n are positive integers. So, the result must be positive integer too. Then, we can check for the perfect square 39 9 2 399^{2} and 40 0 2 400^{2} since it's weird there is a big number 159187 which is very close to 40 0 2 400^{2}

Suradnyana Wisnawa - 6 years, 11 months ago

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