Journal of Integer Sequences, Vol. 11 (2008), Article 08.5.5

On the Number of Subsets Relatively Prime to an Integer

Mohamed Ayad
Laboratoire de Mathématiques Pures et Appliquées
Université du Littoral
F-62228 Calais

Omar Kihel
Department of Mathematics
Brock University
St. Catharines, Ontario L2S 3A1


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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