IJPAM: Volume 70, No. 6 (2011)

THE BEHAVIOR OF DS-DIVISORS OF POSITIVE INTEGERS

Elizabeth Arango$^1$, Aihua Li$^2$
$^1$28, Koenig Court, Fair Lawn, NJ 07410, USA
$^2$Department of Mathematical Sciences
Montclair State University
1, Normal Avenue, Montclair, NJ 07043, USA


Abstract. We study the behavior of DS-divisors of positive integers. Here ``DS" stands for ``divisor-squared." For an integer $n$, a positive divisor $q$ of $n$ is called a DS-divisor if $q^2 \mid n-q$. Such a pair $(n, q)$ is called a DS-pair. Using a table generated for DS-pairs, we examine the existence and the numbers of positive DS-divisors of prime powers, products of two prime powers, and other cases represented by primary factorization. We also investigate patterns and structures of DS-divisors derived from our observations of the table. In addition, we study relationships between the numbers of DS-divisors and the values of Euler function. This research is related to the Primality Test problem of positive integers.

Received: January 24, 2011

AMS Subject Classification: 11B50, 11A51, 11B68

Key Words and Phrases: DS-pair, DS-divisor, Euler number, D-divisibility

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 6