20140820, 22:34  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
4A8_{16} Posts 
problem 2.4
Hi Math People,
Here is another problem from Terence Tao's book Solving Mathematical Problems. Problem 2.4 states  Find all solutions of 2^n + 7 = x^2, where n and x are integers. This one is a little tricky. Regards, Matt 
20140820, 22:57  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23·439 Posts 
Only one solution: n=1, x=3. Consider the equation, modulo 8.

20140821, 03:26  #3 
Jun 2003
5446_{10} Posts 
n = 1, x = 3 ?

20140821, 04:10  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23×439 Posts 
Right, right. x=3.

20140821, 04:40  #5 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{3}·149 Posts 
That is correct. Batalov and Axn are smart cookies.
Regards, Matt 
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