On the Number of Subsets Relatively Prime to an Integer
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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