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

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Wink 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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Old 2014-08-20, 22:57   #2
Batalov
 
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Phi(4,2^7658614+1)/2

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Only one solution: n=1, x=3. Consider the equation, modulo 8.
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Old 2014-08-21, 03:26   #3
axn
 
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n = 1, x = -3 ?
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Old 2014-08-21, 04:10   #4
Batalov
 
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Phi(4,2^7658614+1)/2

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Right, right. |x|=3.
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Old 2014-08-21, 04:40   #5
MattcAnderson
 
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That is correct. Batalov and Axn are smart cookies.

Regards,
Matt
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