For each positive integer n, denote by ω(n) the number of distinct prime divisors of n (for example, ω(1)=0 and ω(12)=2). Find all polynomials P(x) with integer coefficients, such that whenever n is a positive integer satisfying ω(n)>20232023, then P(n) is also a positive integer with
ω(n)≥ω(P(n)).Greece (Minos Margaritis - Iasonas Prodromidis) number theoryBMO 2023gauss lemma