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- Mar 5, 2012

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**Problem statement**

Let n be a whole number of the form [tex]n=x^2+1[/tex] with [tex]x \in Z[/tex], and p an odd prime that divides n.

Proof: [tex]p \equiv 1 \pmod 4[/tex].

**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.

Help?