Related papers: On three problems of Y.--G. Chen

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].

We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.

We hereby reply concisely and hopefully clearly to the ongoing claims of incorrectness made by Chen et al. about our work on two-dimensional flocks.

In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was…

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

In this note, three 2003 problems of Nathanson and two 2007 problems of Chen on unique representation bases for the integers are resolved.

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

In this note we answer the two questions raised by Y.Y Li and L. Nguyen in their note [LN2] below.

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

In this note, we disprove two Romanov type conjectures posed by Chen.

In 1956, Je$\acute{s}$manowicz conjectured that, for positive integers $m$ and $n$ with $m>n, \, \gcd(m,\, n)=1$ and $m\not\equiv n\pmod{2}$, the exponential Diophantine equation $(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z$ has only the positive…

In the present note we prove a multiplicity result for a Kirchhoff type problem involving a critical term, giving a partial positive answer to a problem raised by Ricceri.

We give a new proof of Chen-Lin result with Li-Zhang method.

In this note we prove a weighted version of the Khintchine inequalities.

We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…

In this short note, we give an affirmative answer to Wu's conjecture on practical numbers, which was posed in [X.-H. Wu, {\it Special forms and the distribution of practical numbers}, Acta Math. Hungar., {\bf 160}(2020), 405-411].

In this short note the authors give answers to the three open problems formulated by Wu and Srivastava [{\it Appl. Math. Lett. 25 (2012), 1347--1353}]. We disprove the Problem 1, by showing that there exists a triangle which does not…

This note points out that the assertions of [1] are groundless and incorrect.

We give a sketch for an alternative proof of a recent result by J. Tseng.