Fix coprime natural numbers $a,q$. Assuming the Prime k-tuple Conjecture, we show that there exist arbitrarily long arithmetic progressions of Carmichael numbers, each of which lies in the reduced residue class a mod q and is a product of three distinct prime numbers.

中文翻译：

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残差类别中Carmichael数的算术级数

修正互质自然数 $\mathrm{一种}，q$。假设素数k元组猜想，我们证明了Carmichael数存在任意长的算术级数，每个级数都位于归约残基类别a mod q中，并且是三个不同素数的乘积。