Elementary Number Theory¶
Overview
This article series introduces elementary number theory – the foundation on which the proof of Fermat's Last Theorem is built. We begin with the statement of the famous theorem and work through the first historical proofs for special cases.
What Is This About?¶
Fermat's Last Theorem asserts that the equation
\[
x^n + y^n = z^n
\]
has no solution in positive integers for \(n \geq 3\). For over 350 years this conjecture remained unproven – even though Fermat himself claimed to have found a proof.
In this series we show how the first special cases were solved and why it suffices to prove the theorem only for prime exponents.
Articles in This Series¶
| # | Article | Topic |
|---|---|---|
| 1 | What Is Fermat's Last Theorem? | History, Fermat, 350 years of searching |
| 2 | The Proof for \(n=4\) | Fermat's own proof (Infinite Descent) |
| 3 | Primes and Why They Suffice | Reduction to prime exponents |
| 4 | The Proof for \(n=3\) | Euler, Gauss, algebraic numbers |
Recommended Order¶
The articles build on each other. We recommend reading them in the order listed. Afterwards you will be ready for the Tools of modern mathematics.