Zagier’s one sentence proof

Reference: D. Zagier. “A One-Sentence Proof That Every Prime p \equiv 1(\mod 4) Is a Sum of Two Squares”. The American Mathematical Monthly, vol. 97, no. 2, 1990, pp. 144–144. Link.

Comment

This is the famous “Zagier’s one sentence proof”. I first learned it in an algebra exercise class when I was a third-year student at university. There is a proof in Proofs from THE BOOK .