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March 27th, 2018, 10:28 AM   #1
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Square of a number

Are there infinity natural values of n such that
$\displaystyle 2^n - n $ is a square or
$\displaystyle 2^n - n=p^2$
Example $\displaystyle 2^7 - 7 = 11^2$

Last edited by idontknow; March 27th, 2018 at 10:38 AM.
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March 27th, 2018, 02:56 PM   #2
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n = 0 and n = 1 are also solutions.

Using brute force: no other solutions < 10000
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March 27th, 2018, 06:19 PM   #3
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Quote:
Originally Posted by Denis View Post
n = 0 and n = 1 are also solutions.

Using brute force: no other solutions < 10000
That depends if p is prime or not.
Also using a computer is NOT brute force.
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