Natalia and Marcela counting numbers
Source: II May Olympiad (Olimpiada de Mayo) 1996 L2 P3
September 17, 2022
algebranumber theory
Problem Statement
Natalia and Marcela count by starting together at , but Marcela's speed is triple that of Natalia (when Natalia says her second number, Marcela says the fourth number). When the difference of the numbers that they say in unison is any of the multiples of , between and , Natalia continues counting normally and Marcela begins to count downwards in such a way that, at one point, the two say in unison the same number. What is said number?