## Abstract

Let n be a positive integer and let A be a nonempty finite set of positive integers. We say that A is relatively prime if gcd(A) = 1, and that A is relatively prime to n if gcd(A, n) = 1. In this work we count the number of nonempty subsets of A that are relatively prime and the number of nonempty subsets of A that are relatively prime to n. Related formulas are also obtained for the number of such subsets having some fixed cardinality. This extends previous work for the case where A is an interval of successive integers. As an application we give some identities involving Möbius and Mertens functions, which provide solutions to certain Diophantine equations.

Original language | English |
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Journal | Journal of Integer Sequences |

Volume | 15 |

Issue number | 3 |

Publication status | Published - Mar 25 2012 |

## Keywords

- Combinatorial identities
- Diophantine equation
- Mertens function
- Möbius function
- Phi function
- Relatively prime set

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics