Regular primes, non-Wieferich primes, and finite multiple zeta values of level \(N\) (Q6542788)

For a prime \(p\), we call \(p\) regular when \(p\) is odd and the class number of the \(p\)th cyclotomic field is not divisible by \(p\). We also call \(p\) non-Wieferich when \(2^{p-1}-1\) is not divisible by \(p^2\). It is conjectured that there exist infinitely many regular primes and also non-Wieferich primes. Furthermore, if the latter conjecture is true, then it ensures that the first case of Fermat's last theorem holds for infinitely many prime exponents.\N\NIn this note, the author defines a generalization of finite multiple zeta values to general levels and explore their relationship with the above conjecture. More precisely, he discusses the relationship between the non-zeroness of these values and regular or non-Wieferich primes.