Related papers: An Elementary Proof for Ljunggren Equation
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
In this article we give a result obtained of an experimental way for the Euler totient function.
We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that \[ \binom{a p}{b p} \equiv \binom{a}{b} \] modulo $p^3$ for primes $p\ge5$. This congruence subsumes and builds on earlier congruences by Babbage,…
Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…
These notes are a self-contained short proof of the stability of persistence diagrams.
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm…
We obtain simple proofs of certain inequalites for bivariate means.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We prove a second main theorem for elliptic projective planes.
We give a proof of some small weight and level cases of Serre's conjecture.
In his preprint ``Differential-Geometric Characterizations of Complete Intersections'' (alg-geom/9407002), J.M.Landsberg introduces an elementary characterization of complete intersections. The proof of this criterion uses the method of…
We give a short proof of Ahlfors' theorem on covering surfaces.
There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…
In this short paper we will show, via elementary arguments, the equivalence of the Twin Prime Conjecture to a problem which might be simpler to prove. Some conclusions are drawn, and it is shown that proving the Twin Prime Conjecture is…
We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…
In this paper, the proof of the existence of a rational point on an elliptic curve is transformed into the proof of the existence of an integer solution for a Diophantine equation. By a new formula for calculating the number of elements in…
Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.
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.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
Necessary conditions for a field theoretic equation of motion to be the consequence of variation of an infinite number of inequivalent Lagrangians are examined.