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

Autor: Wayne L. McDaniel
Jazyk: angličtina
Rok vydání: 1990
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 13, Iss 1, Pp 13-24 (1990)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171290000023
Popis: 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).
Databáze: Directory of Open Access Journals
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