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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 $x^{2} - m y^{2} = n$ .

Closed form expressions for several Ramanujan sums

Shader, Leslie E. (1973)

Portugaliae mathematica

Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime $p$ the reduction modulo $p$ of the diagonal of a multivariate algebraic power series $f$ with integer coefficients is an algebraic power series of degree at most $p^{A}$ and height at most $A p^{A}$ , where $A$ is an effective constant that only depends on...

Eine Bemerkung zu einer asymptotischen Formel von Herrn Knopfmacher.

J. Duttlinger (1974)

Journal für die reine und angewandte Mathematik

Equidistribution of linear recurring sequences in finite fields, II

Harald Niederreiter, Jau-Shyong Shiue (1980)

Acta Arithmetica

Explicit form for the discrete logarithm over the field $GF (p, k)$

Gerasimos C. Meletiou (1993)

Archivum Mathematicum

For $a$ generator of the multiplicative group of the field $G F (p, k)$ , the discrete logarithm of an element $b$ of the field to the base $a$ , $b \neq 0$ is that integer $z : 1 \leq z \leq p^{k} - 1$ , $b = a^{z}$ . The $p$ -ary digits which represent $z$ can be described with extremely simple polynomial forms.

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A class of algebraic-exponential congruences modulo $p$ .

A remark on B₂-sequences in GF[p,x]

Abriß einer arithmetischen Theorie der Galoisschen Körper. (Zweite Mitteilung)

Abriß einer arithmetischen Theorie der Galoisschen Körper. (Erste Mitteilung)

An Addition Theorem for the Elementary Abelian Group of Type (p, p).

Applications des corps finis aux nombres pseudo-aléatoires

Arithmetic properties of Bell numbers to a composite modulus I

Arithmetical properties of finite rings and algebras, and analytic number theory.

Barnes' identities and representations of GL (2). I. Finite field case.

Bemerkung zu einem Satz von Glaubermann.

Bounds for digital nets and sequences

Chebyshev polynomials and Pell equations over finite fields

Closed form expressions for several Ramanujan sums

Diagonalization and rationalization of algebraic Laurent series

Eine Bemerkung zu einer asymptotischen Formel von Herrn Knopfmacher.

Equidistribution of linear recurring sequences in finite fields, II

Explicit form for the discrete logarithm over the field $GF (p, k)$

Finite vector spaces and certain lattices.

Gauss sums and the matrix equation $X X^{T} = 0$ over fields of characteristic two

Generalizations of the classical Chebyshev polynomials to polynomials in two variables

Currently displaying 1 – 20 of 65