Related papers: An elementary proof of Fermat's Last Theorem
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.
Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.
We present a short proof of Klartag's central limit theorem for convex bodies, using only the most classical facts about log-concave functions. An appendix is included where we give the proof that thin shell implies CLT. The paper is…
In this note a far extension of the Banach fixed point theorem is proved.
We prove Roth type theorems in finite groups. Our main tool is the Triangle Removal Lemma of Ruzsa and Szemer\'edi.
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
The two squares theorem of Fermat is a gem in number theory, with a spectacular one-sentence "proof from the Book". Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves…
This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring…
We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…
A proof is given of Rosenthal's \(\ell_1\) theorem.
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
The polynomials $x^n + (1-x)^n + a^n$ arise naturally from FLT (Fermat's Last Theorem). We formulate a conjecture about them which is a generalization of FLT. We investigate the complex roots of these polynomials, and our main result is…
Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $\mathbb{Q}$. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
In this paper we obtain new infinite sets of $\zeta$-equivalents of the Fermat-Wiles theorem based on the elementary Fourier orthogonal system, Riemann's zeta-function and Jacob's ladders.