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-   -   problem 2.4 (https://www.mersenneforum.org/showthread.php?t=19620)

MattcAnderson 2014-08-20 22:34

problem 2.4
 
Hi Math People,

Here is another problem from Terence Tao's book [U]Solving Mathematical Problems[/U].

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

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

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


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