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math.NT2025
Carmichael Numbers with a Specified Number of Prime Factors
Daniel Larsen, Thomas Wright
For every sufficiently large integer , there exists a Carmichael number with exactly prime factors.
math.NT2025
Carmichael Numbers in All Possible Arithmetic Progressions
Daniel Larsen
We prove that every arithmetic progression either contains infinitely many Carmichael numbers or none at all. Furthermore, there is a simple criterion for determining which categor…