Related papers: Casas-Alvero Conjecture is true

We show the Graceful Tree Conjecture holds.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

A vector variational principle is proved.

We provide a proof of the Borwein Conjecture using analytic methods.

In this paper, we proved a special case of the DDVV Conjecture.

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

The Casas--Alvero conjecture predicts that every univariate polynomial $f$ over a field $K$ of characteristic zero having a common factor with each of its derivatives $H\_i(f)$ is a power of a linear polynomial. Let…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

In this paper, the abc conjecture is negated under certain conditions

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

A very simple but useful almost sure convergence theorem of probability is given.

Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been…

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].

This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…