March 27th, 2018, 10:28 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 221 Thanks: 26  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. 
March 27th, 2018, 02:56 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,083 Thanks: 795 
n = 0 and n = 1 are also solutions. Using brute force: no other solutions < 10000 
March 27th, 2018, 06:19 PM  #3 
Newbie Joined: Nov 2013 Posts: 26 Thanks: 8  

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