Related papers: An Elementary proof for Bertrand's Postulate
We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreducibility theorem.
We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.
A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
This paper presents a novel direct elementary proof for Fermat's Last Theorem. We use algebra, modular math, and binomial series to develop inherent mathematical relationships hidden within Fermat's Last Theorem. With these derived…
In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.
In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also show that each simple sufficient condition in each statement is…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.
In this note, we prove an analog of the Valiron-Titchmarsch Theorem for Positive Temperatures
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.
The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…
We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree $m$ for Borel measures with moments up to order $m$. The result improves known results for non-compact supports, since we do not need…
We proove a Bloch's theorem in an almost complex projective plane.