Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let (x) be the size of the largest...
: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p − 1] with logr t = t. Here, logr is the d...
We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also...
: We present a modification of the Goldwasser-Kilian-Atkin primality test, which, when given an input n, outputs either prime or composite, along with a certificate of correctnes...
Let Cl(OK [G]) denote the locally free class group, that is the group of stable isomorphism classes of locally free OK [G]-modules, where OK is the ring of algebraic integers in th...