Related papers: An ideal proof for Fujisawa's result and its gener…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We prove the generalized Wolff's Ideal Theorem on certain uniformly closed subalgebras of $ H^{\infty}(\mathbb{D}) $ on which the Corona Theorem is already known to hold.
We give a new simpler proof of a theorem of Jayne and Rogers.
We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.
We present in this work a new and simple proof of the false centre theorem.
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.
The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…
We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for…
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.
We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
It is well known, that Luzin's conjecture has a positive solution for one dimensional trigonometric Fourier series and it is still open for the spherical partial sums $S_\lambda f(x)$, $f\in L_2(\mathbb{T}^N)$, of multiple Fourier series,…
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.