Related papers: Fermat's Last Theorem and its another Proof

Let $K$ be a number field and $p$ a prime number $\geq 5$. Let us denote by $\mu_p$ the group of the $p$th roots of unity. We define $p$ to be $K$-regular if $p$ does not divide the class number of the field $K(\mu_p)$. Under the assumption…

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 short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.

In this paper, we generalized the known Laplace-transform final-value theorem. From our conclusion, one can deduce the existing results in [1, 3, 12]. By using final value theorem, we give a new proof that Caputo fractional differential…

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.

A very simple but useful almost sure convergence theorem of probability is given.

Alpoge and Granville (separately) gave novel proofs that the primes are infinite that use Ramsey Theory. In particular, they use Van der Waerden's Theorem and some number theory. We prove the primes are infinite using an easier theorem from…

In a recent paper, the first author provided some lower bounds to solutions of the equations of Fermat and Catalan, based on local power series developments at the ramified prime of a prime cyclotomic extension. Although both equations have…

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

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…

Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.

We prove the decidability of the elementary theory of a free group.

We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.

For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.

Following the famous proof of Fermat's Last Theorem by Andrew Wiles using the modularity of elliptic curves over $\mathbb{Q}$, significant developments have been made in the study of Diophantine equations using the modularity method. This…

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…