Related papers: An Elementary Proof for Ljunggren Equation

We introduce a Lagrangian which can be varied to give both the equation of motion and world-line deviations of spinning particles simultaneously.

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

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.

We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of independent interest.

We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…

We present an elementary proof of the cross theorem in the case of Reinhardt domains. The results illustrates the well-known interrelations between the holomorphic geometry of a Reinhardt domain and the convex geometry of its logarithmic…

A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a…

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

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

We describe methods to evaluate elementary logarithmic integrals. The integrand is the product of a rational function and a linear polynomial in ln x.

In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…

A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.

We derive the Euler-Lagrange equation corresponding to a variant of non-Euclidean constrained von Karman theories.

We give a closed formula of the Littlewood-Richardson coefficients.

In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.

In \cite{Nam} Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with…

In this paper we show an index theorem for gerbes

In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental…