| 释义 |
Fermat|ˈfɛrma|
The name of Pierre de Fermat (1601–65), French mathematician, used attrib. or in the possessive to designate certain results and concepts introduced by him, as Fermat's last theorem, a famous unproved theorem (of which Fermat said he had ‘a truly wonderful proof’), viz. that if n is an integer greater than 2, xn + yn = zn has no positive integral solutions; Fermat's law = Fermat's principle; Fermat('s) number, a number of the form {two2n} + 1, where n is a positive integer; Fermat's principle, the principle that the path taken by a ray of light between any two points is such that the integral along it of the refractive index of the medium has a stationary value; Fermat's theorem, (a) that if p is a prime number and a an integer not divisible by p, then ap-1 - 1 is divisible by p; (b) = Fermat's last theorem. Also Fermatian |fɜːˈmeɪʃən|, a. and n. (rare).
1811P. Barlow Elem. Invest. Theory of Numbers ii. 48 [This] leads us at once to the demonstration of one of Fermat's theorems, that he considered as one of his principal numerical propositions. 1839Phil. Mag. 3rd Ser. XIV. 48 Horner's extension of Fermat's theorem suggested this extension of Sir John Wilson's to me. 1845Ibid. XXVII. 286 (heading) Proof of Fermat's Undemonstrated Theorem, that xn + yn = zn is only possible in whole numbers when n = 1 or 2. 1865Brande & Cox Dict. Sci., Lit. & Art I. 879/1 Another theorem, distinguished as Fermat's last Theorem, has obtained great celebrity on account of the numerous attempts that have been made to demonstrate it. 1884A. Daniell Text-bk. Physics v. 125 Fermat's Law. 1887J. J. Sylvester in Nature 15 Dec. 153, I have found it useful to denote pi - 1 when p and i are left general as the Fermatian function, and when p and i have specific values as the ith Fermatian of p. 1888Encycl. Brit. XXIV. 424/1 It follows that the course of a ray is that for which the time..is a minimum. This is Fermat's principle of least time. 1906Bull. Amer. Math. Soc. XII. 449 Fermat's numbers..are known to be prime for n = 0, 1, 2, 3, 4, and composite for n = 5, 6, 7, 9, 11, 12, 18, 23, 36, 38. 1948O. Ore Number Theory viii. 204 This is the famous Fermat's theorem, sometimes called Fermat's last theorem, on which the most prominent mathematicians have tried their skill ever since its announcement three hundred years ago. 1959Born & Wolf Princ. Optics 737 The laws of geometrical optics may be derived from Fermat's principle. 1966Ogilvy & Anderson Excurs. Number Theory iii. 36 The higher Fermat numbers have been the subject of prolonged study. |
