Some thoughts on pseudoprimes
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 46 (2021) no. 1
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We consider several problems about pseudoprimes. First, we look at
the issue of their distribution in residue classes. There is a literature
on this topic in the case that the residue class is coprime to the modulus.
Here we provide some robust statistics in both these cases and the general
case. In particular we tabulate all even pseudoprimes to $10^{16}$.
Second, we prove a recent conjecture of Ordowski: the set of integers $n$
which are a pseudoprime to some base which is a proper divisor of $n$
has an asymptotic density.