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Dave Rusin's guide to number theory.
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11: Number theory Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions Elementary number theory involves divisibility among integers the division...Palindrome Quest. Reporting computations on the 196 problem.
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Three Years Of Computing Reverse its digits and add the resulting number to the original number. If the result isn't a palindrome, repeat the process. Do all numbers in base 10 eventually become palindromes through this process? Nobody knows.[1] For example, start with 87....By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.
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Visible Structures in Number Theory Color cover page with abstract Gzip'd PostScript (color 148 kB) Color paperGzip'd PostScript (color 736 kB) Preprint: Submitted for publication 160; ABSTRACT Number theorists have been interested in the characteristics of numerical constants like and for centuries. These numbers, real...To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number. Interactive or via email.
http://www.cecm.sfu.ca/projects/IntegerRelations/
Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.
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Jim Propp's Somos Sequence Site Some conjectures relating to Robinson's work on Somos sequences. A problem (see Fifth Day posed by Don Zagier, in which he states an intriguing possibility (which actually was what motivated Somos in the first place one might re-do the theory...Activated text by Andrew Granville.
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The Arithmetic Properties of Binomial Coefficients Many great mathematicians of the nineteenth century considered problems involving binomial coefficients modulo a prime power (for instance Babbage, Cauchy, Cayley, Gauss, Hensel, Hermite, Kummer, Legendre, Lucas and Stickelberger see Dickson They discovered a variety of elegant and surprising Theorems...Thesis, papers, manuscripts, letters and bibliography.
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Robert Langlands work main page Columbia with an undergraduate degree in 1957 and an M.Sc. in 1958, and from Yale University with a Ph.D. in 1960. He has held faculty positions at Princeton University and Yale University, and is currently a Professor at the Institute...By Paul Garrett.
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Vignettes on automorphic and modular forms, representations, L-functions, and number theory Vignettes on automorphic forms, representations, L-functions, and number theory [ambient page updated 15 Sep 05 home 103 97 114 114 101 116 116 64 109 97 116 104 46 117 109 110 46 101 100 117 Also functional analysis intro...Compiled by Robert Campbell.
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Number Theory Glossary An abelian group is a group whose operation is commutative, ie a*b=b*a. An example of an abelian group is the integers with the usual addition operation. An example of a group which is not abelian is the rotations of a...Related to Somos sequences and elliptic theta functions.
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Somos Polynomials The first observation is that this definition does produce polynomials with positive integer coefficients in the three indeterminates x y z. The proof is by induction. Another observation is that S(n) can be easily extended to n 1 so that...Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.
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Some number-theoretical constants Moree asked me to help with high-precision calculations of some constants arising in various contexts in elementary and analytic number theory. PARI/GP running on a few 333 and 360MHz UltraSPARC-IIi(tm) CPUs soon made short work of them. We pushed the...Algorithm and source code for the calculation of square-free numbers and gaps.
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Square-free Gaps First occurrences of square-free gaps and an algorithm for their computation by Louis Marmet Updated May 18th, 2005 Abstract: This page reports the results of a search for first occurrences of square-free gaps using an algorithm based on the sieve...Classified by degree, then by level, then by eigenvalue, then by root number.
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L-Functions This is the starting point for the L-functions site. In this web site we are interested in giving information about L-functions from the Selberg class S. The information is intended to be both qualitative and quantitative. We intend to list...Email seminar on "Galoissche Theorie der p-Erweiterungen" by Helmut Koch.
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Online Seminar: p-extensions The number theory seminar at CSU San Marcos is devoted this year to a study of the book Galoissche Theorie der p-Erweiterungen Springer 1970, by Helmut Koch. Starting from the basics of profinite groups, Koch gives a self-contained treatment of...Kevin Brown's collection of sci.math postings related to number theory topics.
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MathPages: Number Theory Number Theory Symmetric Pseudoprimes Is e Normal? Identities for Linear Recurring Sequences The Half-Totient Tree Limit Cycles of xy (mod x+y) A Knot of Congruences Rounding Up to PI Fermat's Last Theorem for Cubes Digit Reversal Sums Leading to Palindromes...Index to articles in Eric Weisstein's MathWorld in the area of number theory.
http://mathworld.wolfram.com/topics/NumberTheory.html
Work on the 196 palindrome problem by Tim Irvin.
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About Two Months of Computing After tons of array overruns and lacking motivation to finish the job, the attempt to formulate a program to do the job was abandoned to folks who have time to do such things. My recent job within an aircraft simulation...A test for the terms of a sequence being expressed by a polynomial, by Roupam Ghosh.
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digital root by roupam ghosh introduction hello, my name is roupam ghosh in this site i have stated a theorem that i have found as an application for digital root mail me at:bappan420@yahoo.co.in first we take some basic things into account the digital root of...The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.
http://www.jasondoucette.com/worldrecords.html
Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.
http://members.lycos.co.uk/keithmbriggs/klein-polyhedra.html
A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.
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Covers, Sumsets and Zero-sums This webpage is maintained by Zhi-Wei Sun Please send your comments to zwsun@nju.edu.cn The page has been linked to Number Theory Areas Google Directory: Number Theory and many other web resources. C. Covering Systems (On covers of abelian groups by...Addresses the question whether a series of rational functions converges to a rational number.
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Notes on the attached paper Notes on the attached paper On the convergence of certain infinite processes to rational numbers The paper sets forth simple methods to decide whether an infinite series or other infinite processes would converge to a rational number or an irrational...Things of interest to number theorists collected by Keith Matthews.
http://www.numbertheory.org/ntw/
Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.
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Number Theory Foundation F does not seek to be the sole sponsor of projects, but rather to share in their support. Contributors of substantial donations to the NTF have the opportunity to decide which area or areas of number theory they wish to...Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.
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HAKMEM CONTINUED FRACTIONS DRAFT, NOT YET PROOFED Retyped and converted to html Web browser format) by Henry Baker, April, 1995. CONTINUED FRACTIONS Previous Up Next ITEM 97 (Schroeppel CONTINUED FRACTIONS Simple proofs that certain continued fractions are sqrt(2 sqrt(3 etc. Proof for sqrt(2 X 1, 2, 2,...Proofs along with equation solvers and graphical views written in Java.
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Number Theory Two integer variable equation solver: Diophantine equation ax2 bxy cy2 dx ey f 0 solver, where the unknowns x and y can be integer numbers only. Written in Java/JavaScript. Last updated on May 31st, 2001. Quadratic modular equation solver: Calculator...Michel Waldschmidt. Cetraro summer school lectures, July 2000.
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Cetraro/CIME 2000 Linear Independence Measures for Logarithms of Algebraic Numbers Second 2000 C.I.M.E. Session on Diophantine Approximation, International Mathematical Year Cetraro (Cosenza from June 28 to July 6, 2000. Available as Postscript file, pdf file, dvi file or Zip file. Table of...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.
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Quadratic Reciprocity We describe the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity. The proof is a formalization of an argument due to Eisenstein, based on a lemma of Gauss. We present a...A web article with a brief history and account of their relationship with the Riemann zeta function and Fermat's Last Theorem (HTML/PS).
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Introduction on Bernoulli's numbers Postscript version of this page 1Introduction Bernoulli's numbers play an important and quite mysterious role in mathematics and in various places like analysis, number theory and differential topology. They first appeared in Ars Conjectandi, page 97, a famous (and posthumous)...Maple worksheets, lecture notes and links to other resources by John Cosgrove.
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transcendental numbers I covered only a small part of the very substantial Maple worksheet (along the lines of my Austria 2001 Fermat's little theorem talk) which I prepared for the occasion. The active mws file, with all outputs removed, is available here...A wide selection of number theory topics compiled by Jon Perry.
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Other Maths Curious mod prime relation GCD conjecture Carmichael square root theorem Twin Prime conjecture Germain Primes Perfect Cuboid Mini Erdos-Strauss conjecture Erdos-Strauss conjecture Lucas-Carmichaels Extending Ten Squares Carry Sets Prime Rectangles Prime Rotations Hamiltonian Cycles Hamiltonian Cycles 2 Hamiltonian Cycles 3...Lecture notes and resources on combinatorial number theory by Terence Tao.
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Math 254A Some highlights of arithmetic combinatorics MW 3-4:30, MS 6221 Terence Tao, tao@math.ucla.edu, x64844, MS 5622 A brief summary of the course can be found here. Lecture notes: Lecture notes 1: Cauchy-Davenport inequality, Plunnecke's theorem, sum set estimates. Errata to Q2...With notes on Carmichael numbers and the life of R.D. Carmichael.
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Fermat's Little Theorem Fermat is best know by students is not used nearly so often as the one which is remembered as his little theorem The little theorem is often used in number theory in the testing of large primes and simply states...Number Theory section of the sci.math FAQ list.
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Number Theory What is the current status of FLT? Related Conjectures Did Fermat prove this theorem? Prime Numbers Largest known Mersenne prime Largest known prime Largest known twin primes Largest Fermat number with known factorization Algorithms to factor integer numbers Primality Testing...That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.
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Lehmer's Problem The following problem arises immediately. If is a positive quantity, to find a polynomial of the form f(x xr a1 xr-1 ar where the a's are integers, such that the absolute value of the product of those roots of f...Lecture notes by Alain Connes.
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Course Information In this course we first give a general introduction to noncommutative geometry. We then discuss a fundamental example of noncommutative space related to the Riemann zeta function. This gives a spectral interpretation of the critical zeros of the Riemann zeta...Interactive (Javascript) expression of a number as a sum of two squares.
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Active Elementary Number Theory: n*n 1 and cid-Pairs Script required sequence a...A loosely defined group of individuals, mainly in Canada, active in research in Number Theory.
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The Canadian Number Theory Association Since then there have been several more meetings of CNTA in different locations across Canada, on a somewhat regular basis. The association itself is a loosely defined group of individuals in Canada (and abroad) who are actively doing research in...