MathDB
Lucky groups

Source: China Southeast Math Olympiad 2015 Day 1 P4

June 6, 2017
number theory

Problem Statement

For any positive integer nn, we have the set Pn={nk∣k=0,1,2,…}P_n = \{ n^k \mid k=0,1,2, \ldots \}. For positive integers a,b,ca,b,c, we define the group of (a,b,c)(a,b,c) as lucky if there is a positive integer mm such that a−1a-1, ab−12ab-12, abc−2015abc-2015 (the three numbers need not be different from each other) belong to the set PmP_m. Find the number of lucky groups.
Back to ProblemsView on AoPS