Related papers: Casas-Alvero Conjecture is true
In this note we verify the equivalent version of Huppert's conjecture for $K_3$-groups.
We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$-adic approximation in the spirit of Jarn\'ik and…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
We obtain some results related to Romanoff's theorem.
In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We prove a conjecture due to Y. Last on Jacobi matrices.
We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.
We prove some extensions of Andrews inequality.
We present a conjecture about partitions, with a very elementary formulation.
We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
We prove inversion of adjunction on log canonicity.
In this paper, we give a simple counter example to the famous Hodge conjecture.
In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.
We prove two conjectures on sums of products of Catalan triangle numbers, which were originally conjectured by Miana, Ohtsuka, and Romero [Discrete Math. 340 (2017), 2388--2397]. The first one is proved by using Zeilberger's algorithm, and…