Related papers: An Elementary Proof for Ljunggren Equation

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…

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

We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.

It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.

We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.

We prove the Aharoni Berger Conjecture

We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.

The Integration Theory of Linear Ordinary Differential Equation.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

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

We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

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 will give a simple proof of the ambiguous class number formula.

In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy type of integral estimate on solutions to subcritical Lane-Emden system. To approach the long standing and interesting…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

We find a formula for the number of solutions of linear congruence systems, by using elementary methods.