Pierre de Fermat

Pierre de Fermat (1601–1665) was a lawyer and government official whose mathematical work helped shape number theory, early calculus and probability. His 1654 correspondence with Blaise Pascal on games of chance helped turn questions about fair division of stakes into systematic probability calculations.^[ref]

Fermat's little theorem states that $a^p\equiv a(\mathrm{mod}p)$ for a prime number $p$ and an integer $a$; it gives a reusable arithmetic relation, not a guarantee that every number satisfying one modular test is prime. Fermat's last theorem is the separate assertion that $x^n+y^n=z^n$ has no positive-integer solution for $n>2$. The two statements illustrate the range of his arithmetic questions and must not be conflated with one another or with a proof of the latter assertion by Fermat himself.