THE PAUCITY PROBLEM FOR CERTAIN SYMMETRIC DIOPHANTINE EQUATIONS

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 ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

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.

Diophantine approximation and Diophantine equations

The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...