March 27th, 2018, 10:28 AM  #1 
Senior Member Joined: Dec 2015 From: iPhone Posts: 436 Thanks: 68  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: 14,119 Thanks: 1003 
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: 28 Thanks: 8  

Tags 
number, square 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prove it's a square number?  Tangeton  Number Theory  6  April 15th, 2016 12:51 AM 
Square triangular number  jiasyuen  Number Theory  5  March 10th, 2015 02:57 PM 
Square Number Theorem  M_B_S  Algebra  23  November 20th, 2013 12:01 AM 
about sum of a number to square powers  Dougy  Number Theory  6  June 17th, 2012 07:00 PM 
square number 144...4*1444...44  Cruella_de_Vil  Number Theory  5  March 25th, 2012 06:03 PM 