Biography of Christian Goldbach (1690-1764) ...

Collatz 3n+1 Problem Structure I've finished putting up all the content I can think of concerning a structure I've developed about the Collatz 3n+1 problem. Mathematicians who refer to the problem as the 3x+1 problem were never brainwashed by FORTRAN (as I was) into the belief that n, not x, stands for an integer. I hope someone who can formalize mathematical proofs will see the potential here ...

Plus Online Maths Magazine: Regular Item ...

THE ABC CONJECTURE HOME PAGE La conjecture abc est aussi difficile que la conjecture ... xyz. (P. Ribenboim) The abc conjecture is the most important unsolved problem in diophantine analysis. (D. Goldfeld) Created and maintained by Abderrahmane Nitaj Index The abc conjecture Generalizations Consequences Tables The top ten good abc examples The top ten good abc-Szpiro examples The top ten good ...

Collatz Problem ...

Goldbach conjecture verification Introduction Results References Links Contact Introduction The Goldbach conjecture is one of the oldest unsolved problems in number theory . In its modern form, it states that every even number larger than two can be expressed as a sum of two prime numbers. Let n be an even number larger than two, and let n=p+q, with p and q prime numbers, be a Goldbach partition ...

Computational verification of the 3x+1 conjecture Introduction Results References Links Contact Introduction Let x be an integer. Let the function T(x) be equal to (3x+1)/2 if x is odd and equal to x/2 if x is even. The 3x+1 conjecture , asserts that starting from any positive integer n the repeated iteration of T(x) eventually produces the integer 1, after which the iterates will alternate ...

Ivars Peterson's MathTrek December 8, 1997 The Amazing ABC Conjecture In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer. Fermat's last theorem, for instance, involves an equation of the form x^n + y^n = z^n. More than 300 years ago, Pierre de Fermat (1601-1665) conjectured that ...

A paper by Peter Schorer describing a new approach to the 3x + 1 Problem, an approach based on two remarkably simple structures that underlie the 3x + 1 function. The paper includes a possible solution to the Problem.

International Conference on the Collatz Problem and Related Topics August 5-6, 1999 Katholische Universitat Eichstatt, GERMANY This conference is intended for anyone interested in the 3x+1 problem ( also known as the Syracuse algorithm, Collatz', Kakutani's, or Ulam's problem), and related mathematics. CONFIRMED INVITED SPEAKER: Jeffrey C. Lagarias, AT&T Labs The LOCATION of the conference, ...

The main URL is http://start.at/goldbach/ ...

Information on research on proving the Goldbach Conjecture: that any even number can be represented as the sum of two prime numbers.

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Perfect & Mersenne Numbers The Twin Primes Conjecture & Prime Gaps Fermat Numbers Goldbach's Conjecture Catalan's Conjecture Totient Function Conjectures The Collatz ...

An Image From the Collatz Problem By Andrew Shapira February 15, 1998 (Minor revisions such as web link updates were made subsequently.) Introduction Consider the following rule that maps a given positive integer n to another: if n is even, the next integer is n/2; if n is odd, the next integer is 3n+1. Starting at an arbitrary integer, we can repeatedly apply the rule to obtain a sequence of ...