Day 201 · Jul 19

Birthday of Pierre de Fermat (1601? 1607?)

Pierre de Fermat was a lawyer and amateur mathematician who made profound discoveries. He co‑invented analytic geometry (independently of Descartes), discovered the principle of least time in optics, and laid the foundations of probability theory with Pascal. His ‘little theorem’ (aᵖ≡a mod p for prime p) is a cornerstone of number theory. And his ‘last theorem’ haunted mathematics for 358 years. Fermat rarely published; his ideas survive in letters and marginal notes. He is the patron saint of amateurs who do serious mathematics.

Fermat’s Little Theorem: for prime p, aᵖ ≡ a (mod p). Check with p=7, a=3. Compute 3⁷ and divide by 7 – what is the remainder?

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