M. Seddik

collaborators

3 papers

math.NT2018

Index, Prime Ideal Factorization in simplest Quartic Fields and counting their discriminants

Mohammed Seddik

We consider the simplest quartic number fields $K_{m}$ defined by the irreducible quartic polynomials $x^{4} - m x^{3} - 6 x^{2} + m x + 1,$ where $m$ runs over the positive rational integ…

math.NT2018

Common Divisors of Values Polynomials and common factors of indices in a Number Field

Mohammed Seddik

Let $K$ be a number field of degree $n$ over $Q$ . Let $A$ be the set of integers of $K$ which are primitive over $Q$ and $I(\…

math.NT2018

On cubic Thue equations and the common index divisors of cyclic cubic fields

Mohammed Seddik

In this paper, we investigate the common index divisors of cyclic cubic fields. Let $a, b, c, d$ and $k$ are integers, we then solve the following Thue cubic equations:: \[ax^3+bx^2y+…