On Certain Homogeneous Diophantine Equations of Degree $n(n-1)$

A New Method for Certain Diophantine Equations

1. Introduction. The original purpose of the research described in this article was to obtain results about Diophantine problems on rational surfaces — that is, surfaces defined over a field k which are birationally equivalent to P 2 over the algebraic closure ¯ k. (Throughout this article, K and k will always denote algebraic number fields, with respective rings of integers O and o. Except in ...

On Certain Diophantine Equations in Rings and Fields.

On Certain Diophantine Equations Related to Triangular and Tetrahedral Numbers

In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th International Workshop for Young Mathematicians NUMBER THEORY, Kraków, 14th20th september 2008.

Linear Homogeneous Diophantine Equations and Magic Labelings of Graphs

Degree Computations for Positively Homogeneous Differential Equations

We study 2π-periodic solutions of