Proof p=1 mod 4 if p|x^2+1

  • Thread starter TDA120
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  • #1
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Homework Statement



Let n be a whole number of the form ##n=x^2+1## with ##x \in Z##, and p an odd prime that divides n.
Proof: ##p \equiv 1 \mod 4##.


Homework Equations



The Attempt at a Solution



The only relevant case is if p=3 mod 4.

If I try to calculate mod 3, or mod 4, or mod p, I'm not getting anywhere.
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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Welcome to PF, TDA120! :smile:

Someone gave me a hint: what is the order of x in ##\mathbb{Z}/p\mathbb{Z}^\times##? :wink:

Happy biking!
 

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