Related papers: An Elementary proof for Bertrand's Postulate

In this paper we show an index theorem for gerbes

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.

A proof of Sendov's conjecture is given.

We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

A proof is given of Rosenthal's \(\ell_1\) theorem.

These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

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"

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 present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…

Unlike some other formal systems, the proof system Metamath has no built-in concept of "decimal number" in the sense that arbitrary digit strings are not recognized by the system without prior definition. We present a system of theorems and…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

We present a new, elementary, dynamical proof of the prime number theorem.

In this note we shall give a new proof to a quadrature formulae due to Newton.

In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.