Related papers: An Elementary Proof for the Basel Problem

It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…

An technically interesting proof of a known theorem.

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

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

This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…

By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

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

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

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 new proof of the existence of designs, which is much shorter and gives better bounds.

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

This short note provides and proves an easy algorithm to find a basic feasible solution for the Simplex Algorithm. The method uses a rule similar to Bland's rule for the initial phase of the algorithm.

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.