ACOPS- NT problem

For discussing Olympiad Level Number Theory problems
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bristy1588
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ACOPS- NT problem

Unread post by bristy1588 » Sun Mar 11, 2012 9:13 am

Find all $x$ such that $ x^2+ 2$ is a prime.
Bristy Sikder

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Masum
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Re: ACOPS- NT problem

Unread post by Masum » Wed Mar 14, 2012 12:16 pm

It must say $x$ prime as well. Otherwise it is impossible to find. And then $x=3$ is the only solution since otherwise $x^2+2\equiv1+2\equiv0\pmod3$
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Re: ACOPS- NT problem

Unread post by Moon » Wed Mar 14, 2012 7:33 pm

Umm...actually $x=1,3$. And yeah, mod 3 will do the trick.
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Masum
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Re: ACOPS- NT problem

Unread post by Masum » Wed Mar 14, 2012 10:07 pm

No. :) When you say $x$ is prime.
One one thing is neutral in the universe, that is $0$.

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