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Fermat's Last Theorem

Graduate+

Definition

For integer n ≥ 3, there are no positive integer solutions x, y, z satisfying xⁿ + yⁿ = zⁿ.

xⁿ + yⁿ = zⁿ has no positive integer solutions for n ≥ 3

Example 1

Are there solutions for n = 2?

Discovered by: Pierre de Fermat (conjecture), Andrew Wiles (proof) (1637 (conjecture), 1995 (proof))

Fermat wrote he had a proof in a book margin; Wiles proved it 358 years later.

Elliptic curves, modular forms

Elliptic curve cryptography