Solutions of some classes of congruences

Eugen Vedral

Displaying similar documents to “Solutions of some classes of congruences”

On $p$ -adic zeros of systems of diagonal forms restricted by a congruence condition

Hemar Godhino, Paulo H. A. Rodrigues (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

This paper is concerned with non-trivial solvability in $p$ -adic integers of systems of additive forms. Assuming that the congruence equation $a x^{k} + b y^{k} + c z^{k} \equiv d (m o d p)$ has a solution with $x y z ≢ 0 (m o d p)$ we have proved that any system of $R$ additive forms of degree $k$ with at least $2 \cdot 3^{R - 1} \cdot k + 1$ variables, has always non-trivial $p$ -adic solutions, provided $p ∤ k$ . The assumption of the solubility of the above congruence equation is guaranteed, for example, if $p > k^{4}$ .

Quasi-identities of congruence-distributive quasivarieties of algebras.

Nurakunov, A.M. (2001)

Siberian Mathematical Journal

Similarity:

The Diophantine equation $x^{4} - y^{4} = z^{2}$ in three quadratic fields.

Szabó, Sándor (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Similarity:

On subdirectly irreducible Steiner loops of cardinality $2 n$ .

Armanious, Magdi H. (2002)

Beiträge zur Algebra und Geometrie

Similarity:

A note on a conjecture of Jeśmanowicz

Moujie Deng, G. Cohen (2000)

Colloquium Mathematicae

Similarity:

Let a, b, c be relatively prime positive integers such that $a^{2} + b^{2} = c^{2}$ . Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of ${(a n)}^{x} + {(b n)}^{y} = {(c n)}^{z}$ in positive integers is x=y=z=2. If n=1, then, equivalently, the equation ${(u^{2} - v^{2})}^{x} + {(2 u v)}^{y} = {(u^{2} + v^{2})}^{z}$ , for integers u>v>0, has only the solution x=y=z=2. We prove that this is the case when one of u, v has no prime factor of the form 4l+1 and certain congruence and inequality conditions on u, v are satisfied.