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 March 27th, 2018, 11:28 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 276 Thanks: 32 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 11:38 AM.
 March 27th, 2018, 03:56 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,629 Thanks: 954 n = 0 and n = 1 are also solutions. Using brute force: no other solutions < 10000 Thanks from greg1313
March 27th, 2018, 07:19 PM   #3
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Joined: Nov 2013

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Quote:
 Originally Posted by Denis 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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