Fermat field

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• Fermat's little theorem — (not to be confused with Fermat s last theorem) states that if p is a prime number, then for any integer a , a^p a will be evenly divisible by p . This can be expressed in the notation of modular arithmetic as follows::a^p equiv a pmod{p},!A… …   Wikipedia

• Fermat's factorization method — is based on the representation of an odd integer as the difference of two squares: :N = a^2 b^2. That difference is algebraically factorable as (a+b)(a b); if neither factor equals one, it is a proper factorization of N .Each odd number has such… …   Wikipedia

• Fermat (computer algebra system) — Infobox Software name = Fermat caption = developer = Robert H. Lewis latest release version = 3.9.7 latest release date = May 6 2008 programming language = C operating system = Mac OS X, Mac OS, Linux, Unix, Windows genre = Computer algebra… …   Wikipedia

• Fermat, Pierre de — born Aug. 17, 1601, Beaumont de Lomagne, France died Jan. 12, 1665, Castres French mathematician. Of Basque origin, Fermat studied law at Toulouse and developed interests in foreign languages, Classical literature, ancient science, and… …   Universalium

• Fermat number — In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form:F {n} = 2^{2^{ overset{n} {} + 1where n is a nonnegative integer. The first nine Fermat numbers are OEIS|id=A000215:As of|2008 …   Wikipedia

• Fermat , Pierre de — (1601–1665) French mathematician and physicist Fermat was one of the leading mathematicians of the early 17th century although not a professional mathematician. Born at Beaumont de Lomagne in France, he studied law and spent his working life as a …   Scientists

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Proofs of Fermat's theorem on sums of two squares — Fermat s theorem on sums of two squares asserts that an odd prime number p can be expressed as: p = x^2 + y^2with integer x and y if and only if p is congruent to 1 (mod 4). The statement was announced by Fermat in 1640, but he supplied no proof …   Wikipedia

• Cyclotomic field — In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers. The n th cyclotomic field Q(ζn) (with n > 2) is obtained by adjoining a primitive n… …   Wikipedia

• Pierre de Fermat — Born August 17, 1601( …   Wikipedia

• Método de factorización de Fermat — El método de factorización de Fermat se basa en la representación de un número natural impar como la diferencia de dos cuadrados: n = a2 − b2. Esa diferencia se puede factorizar algebraicamente como (a + b)(a − b); si ninguno de esos factores es… …   Wikipedia Español