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# Product Bases for the Rationals

Published:1999-12-01
Printed: Dec 1999
• P. Berrizbeitia
• P. D. T. A. Elliott
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## Abstract

A sequence of positive rationals generates a subgroup of finite index in the multiplicative positive rationals, and group product representations by the sequence need only a bounded number of terms, if and only if certain related sequences have densities uniformly bounded from below.
 MSC Classifications: 11N99 - None of the above, but in this section 11N05 - Distribution of primes