Problem - 03 - National Math Camp 2021 Number Theory Exam - "Infinitely many prime divisors"
Posted: Thu May 06, 2021 4:32 pm
Let $P(x)$ be a nonzero integer polynomial, that is, the coefficients are all integers. We call a prime $q$ "interesting" if there exists some natural number $n$ for which $q|2^n+P(n)$. Prove that there exist infinitely many “interesting” primes.