Nombres - Numbers

Les "recherches diophantiennes" regroupent des domaines de la théorie des nombres allant de la géométrie diophantienne à la

Robert Munafo

Alternative Number Formats Residue Number System, Double-Base NS, Logarithmic NS, Level-Index (LI) and Symmetric Level-Index (SLI) NS, Alternative Algorithms for Standard Formats, Composite and Hybrid Systems, Arbitrary Precision, General and Survey papers

Fermat's Last Theorem, Graduate Student Number Theory Group, elliptic curves, Lectures and Special Talks, 21 January 1997, Professor Richard Taylor Professor Fred Diamond spoke on 30 January 1997

Patrick De Geest - Belgium

Practical Numbers, Diophantine Approximation (with pictures!!!), Modular Forms, Elementary Number Theory, Random Distribution on Surfaces, Regression L1. Two letters of Erdos

Some Open Diophantine Problems. Algebraic Dynamics and Transcendental Numbers ...

ou RSA généalogie d'un cryptosystème.

Un petit hommage aux arithméticiens de tous les temps de Pythagore à Riemann, en passant par Euclide, Diophante, al-Khorezmi, Fibonnacci, Bachet, Fermat, Euler, Gauss, Lamé et Lucas dont les travaux débouchent sur le cryptosystème de Rivest-Shamir-Adlemman, sans oublier Bézout, Hilbert, Gödel, Peano, Cantor, Turing et von Neuman. Quelques algorithmes sont implantés en TEX, un langage standard pour l´édition scientifique inventé par Knuth.

Philippe Langevin

William Duke

The following notions, definitions, unsolved problems, questions, theorems, corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost primes, mobile periodicals, functions, tables, prime/square/factorial bases, etc. ) have been extracted from the Archives of American Mathematics (University of Texas at Austin), Arizona State University (Tempe): "The Florentin Smarandache papers" special collection, University of Craiova Library, and Arhivele Statului (Filiala Valcea).

To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number

Fred Richman Florida Atlantic University

Andreas Junghans

An Introduction to the Theory of Numbers Oxford University Press. 1979. G. H. Hardy and E. M. Wright.

1.The Romance of Numbers. 2.Doing Arithmetic and Algebra by Geometry. 3.What Comes Next? 4.Famous Families of Numbers. 5.The Primacy of Primes. 6.Further Fruitfulness of Fractions. 7.Algebraic Numbers. 8.Imaginary Numbers. 9.Transcendental numbers. 10.Infinite and infinitesimal numbers.

by Leo Moser

This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate student on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.

About The Trillia Group

by John Brillhart, D.H. Lehmer, J.L. Selfridge, Bryant Tuckerman, and S.S. Wagstaff, Jr. 2002 236pp. Publisher: AMS ISBN:0-8218-3301-4 CONM/ 22.E

Hans Jürgen Prömel

John Horton Conway's theory of surreal numbers is exposed in the form of a play. Two former students lost on a desert island discover pure mathematics and live happily ever after.----Compressed Postscript traduit par Daniel E. Loeb

Felix Kwok July 18, 2001

The problems of cube duplication, angle trisection and circle quadrature are three famous problems that mathematicians have sought to solve since antiquity. In this paper, I will use eld theory to prove that these problems are impossible to solve using the straight edge and compass. It will also be shown that k-sectioning an angle is impossible if k 6 = 2 n for some n. I will also show that only countably many points can be constructed from a nite set of given points. Thus, there will always be real numbers that cannot be constructed.

Laurent Habsieger and Alain Plagne

Ilan Vardi.

Jean COUGNARD (DEA de mathématiques 1998-1999). L

cours

http://www.maths.univ-rennes1.fr/~edix/cours/tano.html

Théorie algébrique des nombres

Les feuilles de TD y sont inclus, ainsi que le partiel et examens. Les résultats fondamentaux de ce cours sont les théorèmes de finitude usuels pour les anneaux d'entiers des corps de nombres: groupe de classes d'idéaux, groupe des unités. Pour ces résultats, le polycopié suit d'assez près le

1. Preliminaries From Commutative Algebra 2. Rings of Integers 3. Dedekind Domains; Factorization 4. The Finiteness of the Class Number 5. The Unit Theorem 6. Cyclotomic Extensions; Fermat's Last Theorem 7. Valuations; Local Fields 8. Global Fields

Knuth up-arrows Conway chains Steinhaus polygons Moser polygons

Didier Dufresnoy a réalisé ce dossier et le graphisme est signé Marc Azra