20140820, 22:34  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
3·367 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
265C_{16} Posts 
Only one solution: n=1, x=3. Consider the equation, modulo 8.

20140821, 03:26  #3 
Jun 2003
23×233 Posts 
n = 1, x = 3 ?

20140821, 04:10  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·5·491 Posts 
Right, right. x=3.

20140821, 04:40  #5 
"Matthew Anderson"
Dec 2010
Oregon, USA
1101_{10} Posts 
That is correct. Batalov and Axn are smart cookies.
Regards, Matt 
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