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

For each integer $n\geq 1$ we consider the unique polynomials $P,Q\in\mathbb{Q}[x]$ of smallest degree $n$ that are solutions of the equation$P(x)x^{n+1}+Q(x)(x+1)^{n+1}=1$. We derive numerous properties of thesepolynomials and their derivatives, including explicit expansions, differentialequations, recurrence relations, generating functions, resultants,discriminants, and irreducibility results. We also consider some relatedpolynomials and their properties.

Arithmetic properties of polynomial solutions of the Diophantine equation $P(x)x^{n+1}+Q(x)(x+1)^{n+1}=1$