## 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} | 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 language | English |
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Pages (from-to) | 785-795 |

Number of pages | 11 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 70 |

Issue number | 6 |

State | Published - 2011 |

## Keywords

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