POLYNOMIALS WITH ROOTS IN Qp FOR ALL p

Let f (x) be a monic polynomial in Z[x] with no rational roots but with roots in Q p for all p, or equivalently, with roots mod n for all n. It is known that f (x) cannot be irreducible but can be a product of two or more irreducible polynomials, and that if f (x) is a product of m > 1 irreducible polynomials, then its Galois group must be a union of… CONTINUE READING