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On the Number of Subsets Relatively Prime to an Integer
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Mohamed Ayad

Laboratoire de Mathématiques Pures et Appliquées

Université du Littoral

F-62228 Calais

France

Omar Kihel

Department of Mathematics

Brock University

St. Catharines, Ontario L2S 3A1

Canada

**Abstract:**

Fix a positive integer and a finite set whose elements are in
arithmetic progression. We give a formula for the number of nonempty
subsets of this set that are coprime to the given integer. A similar
formula is given when we restrict our attention to the subsets having
the same fixed cardinality. These formulas generalize previous results
of El Bachraoui.

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Received October 22 2008;
revised version received December 13 2008.
Published in *Journal of Integer Sequences*, December 13 2008.

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