Arithmetic progressions of arbitrary length and consisting only of primes and almost primes.
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Fix an integer . Rikuna introduced a polynomial defined over a function field whose Galois group is cyclic of order , where satisfies some mild hypotheses. In this paper we define the family of generalized Rikuna polynomials of degree . The are constructed iteratively from the . We compute the Galois groups of the for odd over an arbitrary base field and give applications to arithmetic dynamical systems.