Fermat's equation for matrices or quaternions over q-adic fields

Paulo Ribenboim

doi:10.4064/aa113-3-2

Fermat's equation for matrices or quaternions over q-adic fields

Acta Arithmetica ◽

10.4064/aa113-3-2 ◽

2004 ◽

Vol 113 (3) ◽

pp. 241-250 ◽

Cited By ~ 2

Author(s):

Paulo Ribenboim

Keyword(s):

Fermat's Equation

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On Fermat's Equation in

American Mathematical Monthly ◽

10.1080/00029890.1969.12000334 ◽

1969 ◽

Vol 76 (7) ◽

pp. 808-809

Author(s):

Newcomb Greenleaf

Keyword(s):

Fermat's Equation

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On Fermat’s equation over some quadratic imaginary number fields

Research in Number Theory ◽

10.1007/s40993-018-0117-y ◽

2018 ◽

Vol 4 (2) ◽

Cited By ~ 3

Author(s):

George C. Ţurcaş

Keyword(s):

Number Fields ◽

Imaginary Number ◽

Fermat's Equation

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Fermat's equation over the tower of cyclotomic fields

Izvestiya Mathematics ◽

10.1070/im2001v065n03abeh000337 ◽

2001 ◽

Vol 65 (3) ◽

pp. 503-541

Author(s):

V A Kolyvagin

Keyword(s):

Cyclotomic Fields ◽

Fermat's Equation

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On Fermat's equation with exponent 2p

Colloquium Mathematicum ◽

10.4064/cm-45-1-101-102 ◽

1981 ◽

Vol 45 (1) ◽

pp. 101-102

Author(s):

A. Rotkiewicz

Keyword(s):

Fermat's Equation

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Fermat's Equation Ap+Bp=Cp for Matrices of Integers

Mathematics Magazine ◽

10.1080/0025570x.1972.11976183 ◽

1972 ◽

Vol 45 (1) ◽

pp. 12-15 ◽

Cited By ~ 2

Author(s):

J. L. Brenner ◽

J. De Pillis

Keyword(s):

Fermat's Equation

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A Note on Bernoulli-Goss Polynomials

Canadian Mathematical Bulletin ◽

10.4153/cmb-1984-027-1 ◽

1984 ◽

Vol 27 (2) ◽

pp. 179-184 ◽

Cited By ~ 4

Author(s):

K. Ireland ◽

D. Small

Keyword(s):

Closed Form ◽

Existence Theorem ◽

Function Fields ◽

Bernoulli Polynomials ◽

Bernoulli Polynomial ◽

Computer Search ◽

Quadratic Polynomials ◽

Fermat's Equation

AbstractIn an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l ≤ n ≤ p2-2 we derive a closed form for the nth Bernoulli polynomial. Using this result a computer search for regular quadratic polynomials of the form x2-a was made. For primes less than or equal to 269 regular quadratics exist for p= 3, 5, 7, 13, 31.

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