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Pierre de Fermat (/ f ɜːr ˈ m ɑː /; [2] French: [pjɛʁ də fɛʁma]; 17 August 1601 [a] – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
The Fermat numbers satisfy the following recurrence relations: = + = + for n ≥ 1, = + = for n ≥ 2.Each of these relations can be proved by mathematical induction.From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor greater than 1.
Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a 2 − b 2 . {\displaystyle N=a^{2}-b^{2}.} That difference is algebraically factorable as ( a + b ) ( a − b ) {\displaystyle (a+b)(a-b)} ; if neither factor equals one, it is a proper ...
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam [1] (a Latin treatise circulated in France c. 1636 ) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus.
The Pythagorean equation, x 2 + y 2 = z 2, has an infinite number of positive integer solutions for x, y, and z; these solutions are known as Pythagorean triples (with the simplest example being 3, 4, 5). Around 1637, Fermat wrote in the margin of a book that the more general equation a n + b n = c n had no solutions in positive integers if n ...
Portrait of Pierre de Fermat. Only one mathematical proof by Fermat has survived, in which Fermat uses the technique of infinite descent to show that the area of a right triangle with integer sides can never equal the square of an integer. [1] This result is known as Fermat's right triangle theorem. As shown below, his proof is equivalent to ...
This is a list of things named after Pierre de Fermat, a French amateur mathematician. This list is incomplete; you can help by adding missing items.
The works of the 17th-century mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to a n + b n = c n; Fermat's little theorem, a property of prime numbers; Fermat's theorem on sums of two squares, about primes expressible as a sum of ...