problem 2.4

MattcAnderson · 2014-08-20, 22:34

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

Batalov · 2014-08-20, 22:57

Only one solution: n=1, x=3. Consider the equation, modulo 8.

axn · 2014-08-21, 03:26

n = 1, x = -3 ?

Batalov · 2014-08-21, 04:10

Right, right. |x|=3.

MattcAnderson · 2014-08-21, 04:40

That is correct. Batalov and Axn are smart cookies.

Regards,
Matt

2014-08-20, 22:34	#1
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 800₁₀ 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

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2014-08-20, 22:57	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 Posts	Only one solution: n=1, x=3. Consider the equation, modulo 8.

2014-08-21, 03:26	#3
axn Jun 2003 2²×3×421 Posts	n = 1, x = -3 ?

2014-08-21, 04:10	#4
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	Right, right. \|x\|=3.

2014-08-21, 04:40	#5
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 2⁵×5² Posts	That is correct. Batalov and Axn are smart cookies. Regards, Matt