MathDB
Random prime functions on polynomials

Source: Iranian TST 2021, first exam day 2, problem 4

May 17, 2021
number theorypolynomialprime numbersfunctionalgebraCombi

Problem Statement

Assume Ω(n),ω(n)\Omega(n),\omega(n) be the biggest and smallest prime factors of nn respectively . Alireza and Amin decided to play a game. First Alireza chooses 14001400 polynomials with integer coefficients. Now Amin chooses 700700 of them, the set of polynomials of Alireza and Amin are B,AB,A respectively . Amin wins if for all nn we have : max⁡P∈A(Ω(P(n)))≥min⁡P∈B(ω(P(n)))\max_{P \in A}(\Omega(P(n))) \ge \min_{P \in B}(\omega(P(n))) Who has the winning strategy.
Proposed by Alireza Haghi
Back to ProblemsView on AoPS