Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The least $ r$-free number in an arithmetic progression

Author: Kevin S. McCurley
Journal: Trans. Amer. Math. Soc. 293 (1986), 467-475
MSC: Primary 11B25; Secondary 11N25
MathSciNet review: 816304
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Abstract: Let $ {n_r}(a,q)$ be the least $ r$-free number in the arithmetic progession $ a$ modulo $ q$. Several results are proved that give lower bounds for $ {n_r}(a,q)$, improving on previous results due to Erdös and Warlimont. In addition, a heuristic argument is given, leading to two conjectures that would imply that the results of the paper are close to best possible.

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Article copyright: © Copyright 1986 American Mathematical Society