IMO 2022 Shortlist N3
Let a ą 1 be a positive integer, and let d ą 1 be a positive integer coprime to a. Let x1 “ 1 and, for k ě 1, define xk1...
Category: Number Theory
Problem
Let a ą 1 be a positive integer, and let d ą 1 be a positive integer coprime to a. Let x1 “ 1 and, for k ě 1, define xk`1 “
xk ` d if a doesn’t divide xk, xk{a if a divides xk. Find the greatest positive integer n for which there exists an index k such that xk is divisible by an . (Croatia)