Variations on a Theme of Sierpiński
Department of Mathematics
Shippensburg, Pennsylvania 17257
Using an idea of
Sierpiński proved that there exist
infinitely many odd positive integers k such that
is composite for all positive integers n. In this paper we give a
brief discussion of Sierpiński's theorem and some variations
that have been examined, including the work of Riesel, Brier, Chen,
and most recently, Filaseta, Finch and Kozek. The majority of the
paper is devoted to the presentation of some new results concerning
our own variations of Sierpiński's original theorem.
Full version: pdf,
Received November 14 2006;
revised version received April 14 2007.
Published in Journal of Integer Sequences, April 14 2007.
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