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

Let $a, b\in \mathbb{N}$ be relatively prime. We consider $(a-1)(b-1)/2$,which arises in the study of the $pq$-th cyclotomic polynomial, where $p,q$ aredistinct primes. We prove two possible representations of $(a-1)(b-1)/2$ asnonnegative, integral linear combinations of $a$ and $b$. Surprisingly, foreach pair $(a,b)$, only one of the two representations exists and therepresentation is also unique. We then investigate the representations of$(F_n-1)(F_{n+1}-1)/2$ and $(F_n-1)(F_{n+2}-1)/2$, where $F_i$ is the $i^{th}$Fibonacci number, and observe several nice patterns.

Representation of $\frac{1}{2}(F_n-1)(F_{n+1}-1)$ and $\frac{1}{2}(F_n-1)(F_{n+2}-1)$