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

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data

    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##.


    2. Relevant equations

    3. 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.
     
  2. jcsd
  3. Apr 20, 2012 #2

    I like Serena

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    Homework Helper

    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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