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Displaying 21 – 40 of 197

Arithmetic of Hermitian forms.

Shimura, Goro (2008)

Documenta Mathematica

Berichtigung zu "Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier Quadrate".

Ernst Jacobsthal (1907)

Journal für die reine und angewandte Mathematik

Chebyshev polynomials and Pell equations over finite fields

Boaz Cohen (2021)

Czechoslovak Mathematical Journal

We shall describe how to construct a fundamental solution for the Pell equation $x^{2} - m y^{2} = 1$ over finite fields of characteristic $p \neq 2$ . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation $x^{2} - m y^{2} = n$ .

CHRONIQUE (vol. 1, Fasc. 2.)

(1948)

Colloquium Mathematicae

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

Mollin, R. A. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...

Cobalancing numbers and cobalancers.

Panda, G.K., Ray, P.K. (2005)

International Journal of Mathematics and Mathematical Sciences

Common terms in binary recurrences

Erzsébet Orosz (2006)

Acta Mathematica Universitatis Ostraviensis

The purpose of this paper is to prove that the common terms of linear recurrences $M (2 a, - 1, 0, b)$ and $N (2 c, - 1, 0, d)$ have at most $2$ common terms if $p = 2$ , and have at most three common terms if $p > 2$ where $D$ and $p$ are fixed positive integers and $p$ is a prime, such that neither $D$ nor $D + p$ is perfect square, further $a, b, c, d$ are nonzero integers satisfying the equations $a^{2} - D b^{2} = 1$ and $c^{2} - (D + p) d^{2} = 1$ .

Complete solution of a family of simultaneous Pellian equations

Andrej Dujella (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

Complete solution of the cyclotomic problem in $F_{q}$ for any prime modulus $l, q = p^{α}, p \equiv 1 (m o d l)$

S. Katre, A. Rajwade (1985)

Acta Arithmetica

Congruent numbers with higher exponents

Florian Luca, László Szalay (2006)

Acta Mathematica Universitatis Ostraviensis

This paper investigates the system of equations $x^{2} + a y^{m} = z_{1}^{2}, x^{2} - a y^{m} = z_{2}^{2}$ in positive integers $x$ , $y$ , $z_{1}$ , $z_{2}$ , where $a$ and $m$ are positive integers with $m \geq 3$ . In case of $m = 2$ we would obtain the classical problem of congruent numbers. We provide a procedure to solve the simultaneous equations above for a class of the coefficient $a$ with the condition $gcd (x, z_{1}) = gcd (x, z_{2}) = gcd (z_{1}, z_{2}) = 1$ . Further, under same condition, we even prove a finiteness theorem for arbitrary nonzero $a$ .

Décomposition du carré d’un nombre $N$ et de ce nombre lui-même en sommes quadratiques de la forme $x^{2} + t y^{2}, t$ étant un nombre rationnel, positif ou négatif ; résolution en nombres entiers du système des équations indéterminées $y = x^{2} + t {(x + α)}^{2}, y^{2} = z^{2} + t {(z + β)}^{2}$

E. de Jonquières (1878)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Décomposition du carré d’un nombre N et de ce nombre lui-même en sommes quadratiques de la forme $x^{2} + t \cdot y^{2}, t$ étant un nombre rationnel positif ou négatif ; résolution en nombres entiers du système des équations indéterminées $y = x^{2} + t {(x + α)}^{2}, y^{2} = z^{2} + t {(z + β)}^{2}$

E. de Jonquières (1878)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Currently displaying 21 – 40 of 197

Previous Page 2 Next

Displaying 21 – 40 of 197

Arithmetic of Hermitian forms.

Berichtigung zu "Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier Quadrate".

Chebyshev polynomials and Pell equations over finite fields

CHRONIQUE (vol. 1, Fasc. 2.)

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

Cobalancing numbers and cobalancers.

Common terms in binary recurrences

Complete solution of a family of simultaneous Pellian equations

Complete solution of the cyclotomic problem in $F_{q}$ for any prime modulus $l, q = p^{α}, p \equiv 1 (m o d l)$

Congruent numbers with higher exponents

Constructing fifteen infinite classes of nonregular bipartite integral graphs.

Corps biquadratiques monogènes.

Counting all equilateral triangles in ${0, 1, \dots, n}^{3}$ .

Criterion for 3 to be eleventh power

Démonstration des propositions de M. Lionnet

Développement en fraction continue à l'entier supérieur, idéaux 0-réduits et un problème d'Eisenstein

Diophantine equations of matching games II

Diophantine quadruples for squares of Fibonacci and Lucas numbers.

Currently displaying 21 – 40 of 197