Related papers: On Two of Erd\"os's Open Problems

In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

This note highlights an interesting connection between Euler sums of even weight and prime numbers.

The note complements topological aspects of the theory of chiral algebras.

We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…

This short paper focuses on Schr\"oder's contribute towards a structural view of group theory.

This is a work in two parts devoted to solutions of the so-called {\em four Landau's problems} in Number Theory, listed by Edmund Landau at the 1912 International Congress of Mathematics. In Part I the {\em Goldbach's conjecture} is proved.…

Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…

We propose two distinct interpretations of extended probabilities which are realistic for the physical world.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

An open problem concerning Riemann sums, posed by O. Furdui, is considered.

We give a quintet of proofs resulting from questions posed by Erd\H{o}s. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $K_4$-free $4$-critical graphs with few chords in any…

In this paper we introduce and study a certain type of sub semi-group of $\mathbb{R}/\mathbb{Z}$ which turns out to be closely related to \sz's theorem on arithmetic progressions.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We give a triplet of short proofs, each of which answers a question raised by Erd\H{o}s. The first concerns the small prime factors of $\binom{n}{k}$, the second concerns whether an additive basis $A$ can always be split into pieces $A_1$…

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.