Problem

Source: India Postal Coaching 2014 Set 4 Problem 5 & MR Issue 5,2014

Tags: algebra, polynomial, modular arithmetic, arithmetic sequence, number theory unsolved, number theory



Determine all polynomials $f$ with integer coefficients with the property that for any two distinct primes $p$ and $q$, $f(p)$ and $f(q)$ are relatively prime.