Related papers: An Elementary Proof for Ljunggren Equation

We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian…

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

In this paper we present a short and elementary proof for the error in Simpson's rule.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…

This short note contains elementary evaluations of some Euler sums.

We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

We prove a stability version of the Pr\'ekopa-Leindler inequality.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

A proof of Sendov's conjecture is given.

We give an elementary proof of the Selberg identity for Kloosterman sums, which only requires the orthogonality of additive characters.

We present a conjecture about partitions, with a very elementary formulation.

We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.

Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.

After a brief review of arguments in favor of antigravity (as gravitational repulsion between matter and antimatter) we present a simple idea for an experimental test using antiprotons. Different experimental realizations of the same basic…