Lagrange, central norms, and quadratic Diophantine equations.
Lagrange's Four Squares Theorem with almost prime variables.
Leonard Dickson’s History of the Theory of Numbers: An historical study with mathematical implications
In 1911, the research mathematician Leonard Dickson embarked on a historical study of the theory of numbers which culminated in the publication of his three-volume History of the Theory of Numbers. This paper discusses the genesis of this work, the historiographic style revealed therein, and the mathematical contributions which arose out of it.
Les nombres de Lucas et Lehmer sans diviseur primitif
Y. Bilu, G. Hanrot et P.M. Voutier ont montré que pour toute paire de Lucas ou de Lehmer et pour tout , les entiers, dits nombres de Lucas (ou de Lehmer) admettaient un diviseur primitif. L’objet de ce papier est de compléter la liste des nombres de Lucas et de Lehmer défectueux donnée par P.M. Voutier, afin d’en avoir une liste exhaustive.
Linearly Independent Zeros of Quadratic Forms over Number-Fields.
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains
Let be a 2-dimensional normal excellent henselian local domain in which is invertible and let and be its fraction field and residue field respectively. Let be the set of rank 1 discrete valuations of corresponding to codimension 1 points of regular proper models of . We prove that a quadratic form over satisfies the local-global principle with respect to in the following two cases: (1) has rank 3 or 4; (2) has rank and , where is a complete discrete valuation ring with...
Lower bounds for perfect rational cuboids
Lucas Diophantine triples.