Find the largest possible number of distinct integer values {x_1,x_2,…,x_n}, such that for a fixed reducible degree 4 polynomial with integer coefficients, |f(x_i)| is prime for all i?
If you write p(x) = q(x) r(x)
then either |q(xi)| = 1 or |r(xi)| = 1, the maximum number of points xi is thus 8 if p(x) factors into 2 second degree polynomials or a third degree and a first degree polynomial.