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On the irrationality of Σ (1/(q n+r))

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
37
Issue
3
Identifiers
DOI: 10.1016/s0022-314x(05)80041-1

Abstract

We prove that if q is an integer greater than one and r is a non-zero rational ( r≠ −q m ) then Σ n=1 ∞ (1/( q n + r)) is irrational and is not a Liouville number.

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