16 research outputs found
Non-Wieferich primes in number fields and -conjecture
summary:Let be an algebraic number field of class number one and let be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in under the assumption of the -conjecture for number fields
Non-Wieferich primes in number fields and -conjecture
summary:Let be an algebraic number field of class number one and let be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in under the assumption of the -conjecture for number fields
A short note on number fields defined by exponential Taylor polynomials
Let be a positive integer and denote the -th Taylor polynomial of the exponential
function. Let be an algebraic number field where
is a root of and denote the ring of algebraic
integers of . In this paper, we prove that for any prime , does not
divide the index of the subgroup in if and
only if