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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $\ell, m, r$ be fixed positive integers such that $2\nmid \ell$, $3\nmid\ell m$, $\ell>r$ and $3\mid r$. In this paper, using the BHV theorem on theexistence of primitive divisors of Lehmer numbers, we prove that if$\min\{r\ell m^2-1,(\ell-r)\ell m^2+1\}>30$, then the equation $(r\ellm^2-1)^x+((\ell -r)\ell m^2+1)^y=(\ell m)^z$ has only the positive integersolution $(x,y,z)=(1,1,2)$.

A note on the ternary purely exponential Diophantine equation $A^x+B^y=C^z$ with $A+B=C^2$