Related papers: A simple proof of the Lebesgue decomposition theor…

We give in this note a weighted version of Brianchon-Gram's decomposition for a simple polytope. This weighted version is a direct consequence of the ordinary Brianchon-Gram formula.

A Lebesgue-type decomposition of a (non necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a…

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We present an elementary proof for Ljunggren equation

We generalize the logarithmic decomposition theorem of Deligne-Illusie to a filtered version. There are two applications. The easier one provides a mod $p$ proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a…

The purpose of the paper is to present an short proof of the Chuang's inequality.

Using nonstandard analysis, a very short and elementary proof of the Doob-Meyer decomposition and the Dol{\'e}ans Dade theorems is provided.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the…

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

A very short proof of Kneser's theorem via transversal is given.

In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.

We provide a short proof of the 1-dimensional flat chain conjecture.

The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

This note contains a short proof of the functional equation for the zeta function.

We present in this work a new and simple proof of the false centre theorem.