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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We show that there exists a natural extention of the sum of divisors function to all unique factorization domains F having a finite number of units such that if a perfect number in F is defined to be an integer η whose proper divisors sum to η, then the analogue of  Euclid's theorem giving the sufficient condition that an integer be an even perfect number holds in F, and an analogue of the Euclid-Euler theorem giving the necessary and sufficient condition that an even integer be perfect holds in those domains having more than two units, i. e., in Q(−1) and Q(−3)

An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers