Number Theory

A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.

A paper by David M. Russinoff describing the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity. PS/PDF.

Algorithm and source code for the calculation of square-free numbers and gaps.

By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.

Formulae and tables for the number of non isomorphic fields with a fixed signature and Galois group sharing a common discriminant.

Taken by Sean Sather-Wagstaff, Utah, Spring 1999. In PS and PDF formats.

Lecture Notes by Noam Elkies, Harvard, 1998.

Archives of postings to the Number Theory mailing list (NMBRTHRY).

Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.

Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

Some of conjectures and open problems, compiled at AIM.

A web tool for solving Diophantine equations of the form ax + by = c.

Lecture Notes by Don Rideout, Memorial University of Newfoundland. PDF and Maple worksheets.

By Kenneth Kramer, Queens College (CUNY). Abstract with text in PDF.

Courses in Number Theory at St Patrick's College, Dublin.

An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.

Programme at MSRI, Berkeley; January-May 2014.

Held at the Archives of American Mathematics, Center for American History, University of Texas at Austin.

Unsolved Problems in Number Theory, Logic and Cryptography, with references for further reading.

Members, publications, activities.

Carlos Rivera's collection of problems and puzzles related to prime numbers.

The "Riesel Prime Search" project is searching for primes of the form k·2^n-1, odd k.

Number Theory and Algebraic Geometry Research Group. Members, research interest, seminars.

A European network of 12 working groups from 6 countries.

Number Theory Group. Members, publications, meetings.

KANT is a software package for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell.

EIS-Seeker is a libguile-based scheme interpreter devoted to the study of the Encyclopedia of Integer Sequences database. It is intended to help find new relations between sequences. C/Scheme, Posix.

R. Ernvall and T. Metsänkylä. Tables of the pairs (p,k) such that the Fermat quotient q(k) = (k^{p-1}-1)/p vanishes mod p. The tables cover the primes p up to one million and, for each prime, the range 1 < k < p.

Noam Elkies. Approximate solutions in integers.

NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on Sophie Germain, and the Pythagorean theorem.

Article in Eric Weisstein's World of Mathematics.

For each curve (labelled as in Cremona) the mu and lambda-invariants are listed for the primes between 2 and 17. By Robert Pollack.

Workshop on recent developments. Far Hills Inn, near Montreal, Canada; 3--6 January 2002.

University of Illinois at Urbana-Champaign, USA; 21--22 May 2004.

Canadian Number Theory Association VIIIth meeting. Toronto, Ontario; 20--25 June 2004.

Strobl, Austria; 27 September -- 1 October 2004.

Prof. Carl Pomerance. University of British Columbia, Vancouver, BC, Canada; 21--23 March 2005.

Georg-August-Universität, Göttingen, Germany; 20--24 June 2005.

AIM Research Conference Center, Palo Alto, CA, USA; 15--19 August 2005.

International conference on Diophantine Equations in honour of Professor T.N. Shorey on his 60th Birthday. TIFR, Mumbai, India; 16--20 December 2005.

Held as part of FoCM'05. University of Cantabria, Santander, Spain; 7--9 July 2005.

XXIIIrd Journées Arithmétiques. Graz, Austria; 6--12 July 2003.

Algorithmic Number Theory Program, MSRI, 11-15 December 2000, Berkeley.

Banff International Research Station, Alberta, Canada; 15--19 May 2006.

Meets regularly in Massachusetts. Programme, some abstracts.

Maintained by Abderrahmane Nitaj.

Brief article offers a description of the problem and features links.

A brief popular article with an applet generating solutions.

MathWorld article and resources.

Lawrence Berkeley National Laboratory. Experimental mathematics and scientific computing. Research papers, photos, and links.