Related papers: A Proof of Kamp's theorem
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
We prove an infinitary version of the Brauer-Schur theorem.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
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.
The purpose of the paper is to present an short proof of the Chuang's inequality.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.
We define a category whose objects are finite etale coverings of an algebraic stack and prove that it is a Galois category and that it allows one to compute the fundamental group of the stack. We then prove a Van Kampen theorem for…
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.
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.
We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We obtain simple proofs of certain inequalites for bivariate means.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We describe two distinct simple, short and self contained proofs of the composition lemma.
We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.