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

We give an historical account, including recent progress, on some problems of Erd\H os in number theory.

In this note we briefly survey and propose some open problems related to isoparametric theory.

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

This is a survey of some of Erd\H os's work on bases in additive number theory.

This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.

I state some open problems coming from joint work with Paul Erd\H{o}s

We survey some recent developments and give a list of open problems regarding multiple recurrence and convergence phenomena of $\mathbb{Z}^d$ actions in ergodic theory and related applications in combinatorics and number theory.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

This is a short note about a chapter in the author's bachelor thesis regarding a paper by Ford concerning a conjecture by Erd\H{o}s.

This is a short survey article written for the Erd\H{o}s centennial conference in Budapest in 2013. The main two topics covered are Szemer\'edi's theorem and its ramifications, and the Erd\H{o}s discrepancy problem. There is an emphasis on…

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

Work in progress concerning alternative formalizations of arithmetic.

We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…

This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…

We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.

The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.