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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
DOI: https://doi.org/10.1090/S0002-9947-1986-0816304-1
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0816304-1
Article copyright: © Copyright 1986 American Mathematical Society

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