Geodesic
Carmichael numbers composed of primes from a Beatty sequence
William D. Banks 1   ; Aaron M. Yeager 2
1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
2 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A. \emailaut2{amydm6@mail.missouri.edu
Colloquium Mathematicum, Tome 125 (2011) no. 1, pp. 129-137 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\alpha,\beta\in\mathbb R$ be fixed with $\alpha>1$, and suppose that $\alpha$ is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence $\mathscr B_{\alpha,\beta}=(\lfloor{\alpha n+\beta}\rfloor)_{n=1}^\infty$. We conjecture that the same result holds true when $\alpha$ is an irrational number of infinite type.
DOI : 10.4064/cm125-1-9
Keywords: alpha beta mathbb fixed alpha suppose alpha irrational finite type there infinitely many carmichael numbers composed solely primes non homogeneous beatty sequence mathscr alpha beta lfloor alpha beta rfloor infty conjecture result holds alpha irrational number infinite type

William D. Banks  1   ; Aaron M. Yeager  2

1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
2 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A. \emailaut2{amydm6@mail.missouri.edu 
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William D. Banks; Aaron M. Yeager. Carmichael numbers composed of primes from a Beatty sequence. Colloquium Mathematicum, Tome 125 (2011) no. 1, pp. 129-137. doi: 10.4064/cm125-1-9

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