One curious proof of Fermat's little theorem

TL;DR

This paper presents a humorous yet rigorous proof of Fermat's little theorem using formal power series, avoiding traditional arithmetic and algebraic methods.

Contribution

It introduces a novel proof technique for Fermat's little theorem leveraging formal power series instead of standard algebraic or arithmetic approaches.

Findings

Provides a rigorous proof of Fermat's little theorem

Demonstrates an unconventional proof method using formal power series

Highlights the playful nature of mathematical proofs

Abstract

We give a proof of Fermat's little theorem which does not use nor arithmetic(Euclidean algorithm) neither algebra (group theory), but it rather employs the field of the formal power series Q((x)). The note is an example of a mathematical joke, though it contains a rigorous proof. (The paper will appear in print exactly as in the version v3).