Related papers: A new method to prove the Collatz conjecture

We motivate and explain the system introduced by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used…

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…

Lorenz equations were first presented in 1963 by Edward Lorenz, they depend on three real positive parameters. For some of these parameters which are called T-points, there are two heteroclinic orbits connecting the three singular points in…

In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We then prove our main result about the…

We aim to prove a twisted version of the Osborne conjecture obtained by Hecht and Schmid in their 1983 Acta Mathematica paper. Bergeron and Clozel (2013) have considered a special case, and we generalize their method to our setting.

In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named author in 1978.

The Riemann hypothesis is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems. it is also one of the Clay Mathematics Institute's Millennium Prize Problems. Some mathematicians consider it the most important…

In this article, we shall describe some of the most interesting topics in the subject of Complexity Science for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary…

Sequence of numbers generated by the recurrence relation based on the Collatz conjecture is investigated. An arithmetic operation on the Collatz conjecture is called descending operation, and ascending operation is carried out reversely to…

This paper gives a counterexample to the impossibility, by G\"odel's second incompleteness theorem, of proving a formula expressing the consistency of arithmetic in a fragment of arithmetic on the assumption that the latter is consistent.…

In this article we present set of infinite natural numbers which satisfies the conjecture $3n+1$.

The Lambert W function was introduced by Euler in 1779, but was not well-known until it was implemented in Maple, and the seminal paper of Corless, Gonnet, Hare, Jeffrey and Khuth was published in 1996. In this note we describe a simple…

Einstein's famous 1938 experiment to test relativity of time is plagued by too many ambiguities and does not prove anything. Nevertheless, it is a landmark experiment at the foundation of the modern theory of time perception.

Let $g$ be a map from the set of positive integers into itself defined as follows: Let $x$ be a positive integer. If $x$ is odd, then $g(x)=3x+1$, and if $x$ is even, then $g(x)=x/2$. The $3x+1$ conjecture, also called the Collatz…

In his book \emph{Topics in Analytic Number Theory}, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of…

In 1995, Meinardus & Berg presented a reformulation of the Collatz Conjecture in terms of a functional equation in a single complex variable over the open unit disk. This paper generalizes that method to deal with not only a large class of…

The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most…

This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].