IMO 2024 Shortlist N6
Let n be a positive integer. We say that a polynomial P with integer coeffi- cients is n-good if there exists a polynomi...
Category: Number Theory
Problem
Let n be a positive integer. We say that a polynomial P with integer coeffi- cients is n-good if there exists a polynomial Q of degree 2 with integer coefficients such that QpkqpPpkq ` Qpkqq is never divisible by n for any integer k. Determine all integers n such that every polynomial with integer coefficients is an n-good polynomial. (France)