The behavior of DS-divisors of positive integers

Elizabeth Arango, Aihua Li

Research output: Contribution to journalArticlepeer-review


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 q2 | 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.

Original languageEnglish
Pages (from-to)785-795
Number of pages11
JournalInternational Journal of Pure and Applied Mathematics
Issue number6
StatePublished - 2011


  • D-divisibility
  • DS-divisor
  • DS-pair
  • Euler number


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