相关论文: A proof of Sendov's conjecture

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

We prove a conjecture of Meszaros and Morales on the volume of a flow polytope. Independently from our work, Zeilberger sketched a proof of their conjecture. In fact, our proof is the same as Zeilberger's proof. The purpose of this note is…

We give a new proof of Lucas' Theorem in elementary number theory.

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

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We prove inversion of adjunction for higher rational singularities.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

In this note, we prove Veselov's conjecture on the zeros of Wronskians whose entries are Hermite polynomials when the degrees of the polynomials are consecutive positive integres.

We prove an infinitary version of the Brauer-Schur theorem.

In this paper, we prove a congruence which confirms a conjecture of Adamchuk. For any prime $p\equiv1\pmod3$ and $a\in\mathbb{Z}^{+}$, we have \begin{align*} \sum_{k=1}^{\frac{2}3(p^a-1)}\binom{2k}k\equiv0\pmod{p^2}. \end{align*}

Several results about the union-closed sets conjecture are presented.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

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

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

We give an elementary proof to Hasse theorem.

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].

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.