English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This study investigates the existence of tuples $(k, \ell, m)$ of integerssuch that all of $k$, $\ell$, $m$, $k+\ell$, $\ell+m$, $m+k$, $k+\ell+m$ belongto $S(\alpha)$, where $S(\alpha)$ is the set of all integers of the form$\lfloor \alpha n^2 \rfloor$ for $n\geq \alpha^{-1/2}$ and $\lfloor x\rfloor$denotes the integer part of $x$. We show that $T(\alpha)$, the set of all suchtuples, is infinite for all $\alpha\in (0,1)\cap \mathbb{Q}$ and for almost all$\alpha\in (0,1)$ in the sense of the Lebesgue measure. Furthermore, we showthat if there exists $\alpha>0$ such that $T(\alpha)$ is finite, then there isno perfect Euler brick. We also examine the set of all integers of the form$\lceil \alpha n^2 \rceil$ for $n\in \mathbb{N}$.

A system of certain linear Diophantine equations on analogs of squares