3 papers
math.NT2026
Robust additive bases without minimal subbases
Daniel Larsen, Michael Larsen
There exists a set of positive integers such that the number of representations of a large positive integer as a sum of two elements of grows with a lower bound of orde…
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…