Some trigonometric identities related to exact covers

Author:
John Beebee

Journal:
Proc. Amer. Math. Soc. **112** (1991), 329-338

MSC:
Primary 11B25; Secondary 11L03

MathSciNet review:
1049133

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Abstract | References | Similar Articles | Additional Information

Abstract: Sherman K. Stein proves that if where the are integers, the are positive integers, is a constant, then is an exact cover. It is shown here that if then , that the converse is also true, and an analogous formula is conjectured for infinite exact covers. Many well known and lesser known trigonometric and functional identities can be derived from this result and known families of exact covers. A procedure is given for constructing exact covers by induction.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1049133-4

Keywords:
Exact covering systems,
functional identities,
trigonometric identities

Article copyright:
© Copyright 1991
American Mathematical Society