The least 𝑟-free number in an arithmetic progression

McCurley, Kevin S.

doi:10.1090/S0002-9947-1986-0816304-1

The least $r$-free number in an arithmetic progression
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by Kevin S. McCurley PDF

Trans. Amer. Math. Soc. 293 (1986), 467-475 Request permission

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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