An Unimaginative Proof of Fermat's Two Squares Theorem

2025/08/13 by Bachman, Gennady
#11A41 #11E25 #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.10234

Abstract

We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students who are just starting out in math.

Citations

• A Quixotic Proof of Fermat's Two Squares Theorem for Prime Numbers

Related

• A Quixotic Proof of Fermat's Two Squares Theorem for Prime Numbers
• Fermat's Last Theorem and its another Proof
• Formal verification of Zagier's one-sentence proof
• Diophantus' 20th Problem and Fermat's Last Theorem for n=4: Formalization of Fermat's Proofs in the Coq Proof Assistant
• Orthogonal matrices with rational components in composing tests for High School students