Prime factors of af(n)-1 with an irreducible polynomial f(x)

摘要

In this note, we show that if a is an integer not 0 or ±1 and f(X)∈ Q[X] is an integer valued irreducible polynomial of degree d≧ 2, then the set of primes p dividing af(n)-1 for some positive integer n is of (relative) asymptotic density zero.