Related papers: An Elementary Proof for Ljunggren Equation

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…

We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.

Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.

In this paper, we present a short proof of Halin's grid theorem.

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].

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We offer elementary proofs for fundamental properties of the unique triple-zero solution to the first Painlev\'e equation.

The aim of this paper is to write explicit expression in terms of a given principal connection of the Lagrange-d'Alembert-Poincar\`{e} equations in several stages. This is obtained by using a reduced Lagrange-d'Alembert's Principle in…

We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…

Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible…

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

We give simple proofs for the Hankel determinants of q-exponential polynomials.

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

We give a new elementary proof of the following theorem: if all critical points of a rational function g belong to the real line then there exists a fractional linear transformation L such that L(g) is a real rational function. Then we…