mersenneforum.org problem 2.4
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 2014-08-20, 22:34 #1 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 32·131 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
 2014-08-20, 22:57 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×33×5×37 Posts Only one solution: n=1, x=3. Consider the equation, modulo 8.
 2014-08-21, 03:26 #3 axn     Jun 2003 34·67 Posts n = 1, x = -3 ?
 2014-08-21, 04:10 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·33·5·37 Posts Right, right. |x|=3.
 2014-08-21, 04:40 #5 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 22338 Posts That is correct. Batalov and Axn are smart cookies. Regards, Matt

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