相关论文: A Short Proof of the Poincar\'e Conjecture
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
An proof of Poincare Duality with local coefficients and with compact support is provided. The proof does not require Sheaf Theory or anything equivalent and is thus more accessible for the general audience.
In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
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 paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to…
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
Gives a short proof of Dehornoy's latest result. The same simple argument (and more) was discovered by Laver's student Larue.
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…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using…
We obtain simple proofs of certain inequalites for bivariate means.
We make an attempt at proving the Four Colour Theorem in six pages.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
This paper has been withdrawn by the authors due to an error in Section 7.
We provide a simple proof of Kamp's theorem.
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.
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.