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Carmichael numbers composed of primes from a Beatty sequence

William D. BanksAaron M. Yeager — 2011

Colloquium Mathematicae

Let α,β ∈ ℝ be fixed with α > 1, and suppose that α 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 α , β = ( α n + β ) n = 1 . We conjecture that the same result holds true when α is an irrational number of infinite type.

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