Fermatn.

Brit.

/ˈfəːmɑː/,

/fəˈmat/,

/ˈfəːmat/, U.S.

/fərˈmɑ/,

/fərˈmɑt/

Etymology: < the name of Pierre de Fermat (1601–65), French mathematician.

Used attributively or in the possessive to designate certain results and concepts introduced by Fermat, as Fermat's last theorem, a famous theorem that went unproved until 1994 (Fermat having claimed that he had a ‘truly wonderful proof’ without ever disclosing it), 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 2^2ⁿ + 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 a^p−1 − 1 is divisible by p; (b) = Fermat's last theorem at main sense.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to prime numbers

Fermat's theorem1811

Sylow's theorem1893

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem

pons asinorum1718

Fermat's theorem1845

Bernoulli's theorem1865

Fermat's last theorem1865

Fourier's theorem1880

remainder theorem1886

Stokes' theorem1893

Jordan('s) (curve) theorem1900

Waring's theorem1920

Gödel's theorem1933

maximin1953

incompleteness theorem1955

Schwarz inequality1955

the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > prime > relating to

Mersenne1892

Fermat('s) number1906

twin prime1930

pseudoprime1949

Skewes1949

1811 P. 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.

1839 London & Edinb. Philos. Mag. 14 48 Horner's extension of Fermat's theorem suggested this extension of Sir John Wilson's to me.

1845 London, Edinb. & Dublin Philos. Mag. 3rd. Ser. 27 286 (heading) Proof of Fermat's Undemonstrated Theorem, that xⁿ + yⁿ = zⁿ is only possible in whole numbers when n = 1 or 2.

1865 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) 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.

1884 A. Daniell Text-bk. Princ. Physics v. 125 Fermat's Law.

1888 Encycl. 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.

1906 Bull. Amer. Math. Soc. 12 449 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.

1948 O. 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.

1959 M. Born & E. Wolf Princ. Optics 737 The laws of geometrical optics may be derived from Fermat's principle.

1966 C. S. Ogilvy & J. T. Anderson Excursions Number Theory iii. 36 The higher Fermat numbers have been the subject of prolonged study.

Derivatives

Fermatian adj. and n.

/fɜːˈmeɪʃən/ (rare).

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to

physico-mathematical1660

analytical1694

Bernoulli1749

analytic1761

Boolean1851

Sturmian1853

Bernoullian1876

Fermatian1887

Grassmannian1894

number-theoretic1899

Cantor1902

Cantorian1912

Tauberian1913

Thiessen1923

intuitionist1926

metamathematical1926

finitist1931

number-theoretical1936

finitistic1937

proof-theoretic1940

formalistic1941

Gödelian1942

constructivist1943

constructivistic1944

game-theoretical1946

game-theoretic1950

finitary1952

perturbation-theoretic1964

perturbation-theoretical1968

constructive1979

1887 J. 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.

This entry has not yet been fully updated (first published 1972; most recently modified version published online March 2022).

单词	fermat
释义	Fermatn. Brit. /ˈfəːmɑː/, /fəˈmat/, /ˈfəːmat/, U.S. /fərˈmɑ/, /fərˈmɑt/ Etymology: < the name of Pierre de Fermat (1601–65), French mathematician. Used attributively or in the possessive to designate certain results and concepts introduced by Fermat, as Fermat's last theorem, a famous theorem that went unproved until 1994 (Fermat having claimed that he had a ‘truly wonderful proof’ without ever disclosing it), 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 2^2ⁿ + 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 a^p−1 − 1 is divisible by p; (b) = Fermat's last theorem at main sense. ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to prime numbers Fermat's theorem1811 Sylow's theorem1893 the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem pons asinorum1718 Fermat's theorem1845 Bernoulli's theorem1865 Fermat's last theorem1865 Fourier's theorem1880 remainder theorem1886 Stokes' theorem1893 Jordan('s) (curve) theorem1900 Waring's theorem1920 Gödel's theorem1933 maximin1953 incompleteness theorem1955 Schwarz inequality1955 the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > prime > relating to Mersenne1892 Fermat('s) number1906 twin prime1930 pseudoprime1949 Skewes1949 1811 P. 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. 1839 London & Edinb. Philos. Mag. 14 48 Horner's extension of Fermat's theorem suggested this extension of Sir John Wilson's to me. 1845 London, Edinb. & Dublin Philos. Mag. 3rd. Ser. 27 286 (heading) Proof of Fermat's Undemonstrated Theorem, that xⁿ + yⁿ = zⁿ is only possible in whole numbers when n = 1 or 2. 1865 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) 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. 1884 A. Daniell Text-bk. Princ. Physics v. 125 Fermat's Law. 1888 Encycl. 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. 1906 Bull. Amer. Math. Soc. 12 449 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. 1948 O. 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. 1959 M. Born & E. Wolf Princ. Optics 737 The laws of geometrical optics may be derived from Fermat's principle. 1966 C. S. Ogilvy & J. T. Anderson Excursions Number Theory iii. 36 The higher Fermat numbers have been the subject of prolonged study. Derivatives Fermatian adj. and n. /fɜːˈmeɪʃən/ (rare). ΘΚΠ the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to physico-mathematical1660 analytical1694 Bernoulli1749 analytic1761 Boolean1851 Sturmian1853 Bernoullian1876 Fermatian1887 Grassmannian1894 number-theoretic1899 Cantor1902 Cantorian1912 Tauberian1913 Thiessen1923 intuitionist1926 metamathematical1926 finitist1931 number-theoretical1936 finitistic1937 proof-theoretic1940 formalistic1941 Gödelian1942 constructivist1943 constructivistic1944 game-theoretical1946 game-theoretic1950 finitary1952 perturbation-theoretic1964 perturbation-theoretical1968 constructive1979 1887 J. 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. This entry has not yet been fully updated (first published 1972; most recently modified version published online March 2022). < n.1811
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