Related papers: A new method to prove the Collatz conjecture

The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…

The letter reminds the historical fact that the known "Lorenz gauge" (or "Lorenz condition/relation") is first mentioned in a written form and named after Ludwig Valentin Lorenz and not by/after Hendrik Antoon Lorentz.

In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. C\'ordoba in 1978. Our approach avoids a subtle argument involving the…

The inverse problem of Galois Theory was developed in the early 1800 s as an approach to understand polynomials and their roots. The inverse Galois problem states whether any finite group can be realized as a Galois group over Q (field of…

The purpose of this study is to show how to get a necessary criterion for prime numbers with the help of special matrices. My special interest lies in the empirical research of these matrices and their patterns, structures and symmetries.…

In 1956 Hirzebruch found an explicit formula for the denominators of the Todd polynomials, which was proved later in his joint work with Atiyah. We present a new formula for the Todd polynomials in terms of the ``forgotten symmetric…

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951{2001). This approach also indicates some…

This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history,…

We prove a conjecture by D. Zeilberger on the determinant of a certain matrix and relate it to a problem of non-existence of 1-cycles in this note.

In this paper two conjectures are proposed based on which we can prove the first case of Fermat's Last Theorem(FLT) for all primes $p \equiv -1 (\bmod~6)$. With Pollaczek's result {\bf [1]} and the conjectures the first case of FLT can be…

"Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers.

I present and discuss a puzzle about wizards invented by John H. Conway.

The Goldbach conjecture that, every even integer is the sum of two primes, has been open since 1742. This paper details a road map to a proof of Goldbachs conjecture based on a function that estimates the number of Goldbach pairs. It is…

The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.

We give a new proof of Carlitz-Wan's conjecture, previously proved by Lenstra (1995).Our proofs are natural and intuitive, and shed new insights into the study of exceptional polynomials.

Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…

Very recently, Qi and Cui extended the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts and proved that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz method…

The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…

The theory of the calculus of variations for fuzzy systems was recently initiated in [7], with the proof of the fuzzy Euler-Lagrange equation. Using fuzzy Euler-Lagrange equation, we obtain here a Noether-like theorem for fuzzy variational…