He invented a factorization method—Fermat's factorization method—and popularized the proof by infinite descent, which he used to prove Fermat's right triangle theorem which includes as a corollary Fermat's Last Theorem for the case n = 4.

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Pierre de Fermat (born August 17, 1601, Beaumont-de-Lomagne, France—died January 12, 1665, Castres) was a French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes , Fermat was one of the two leading mathematicians of the first half of the 17th century.

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2.

Fermat mathematician made significant contributions to number theory, probability theory, analytic geometry and the early development of infinitesimal calculus. He ventured into the areas of mathematics which included pre-evolved calculus and trigonometry.

In mathematics, a Fermat number, named after Pierre de Fermat (1607–1665), the first known to have studied them, is a positive integer of the form: = +, where n is a non-negative integer.

Fermat is a computer algebra system for Macintosh, Windows, Linux, and Unix by me, Robert H. Lewis of Fordham University, that does arithmetic of arbitrarily long integers and fractions, multivariate polynomials, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations. It is extremely fast and extremely ...

Pierre de Fermat, effectively invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician.

Fermat’s Last Theorem: Perhaps Fermat’s most famous contribution, this theorem posits that there are no positive integer solutions to the equation \(x^n+y^n=z^n\) for \(n>2\). Fermat claimed to have a “marvelous proof” that was too large to fit in the margin of his notebook.