MathDB
f(n+1) = f(n)-2n+43$

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p4

March 26, 2024
algebrafunctionfunctional equation

Problem Statement

Maria was a brilliant mathematician who found the following property about her year of birth: if ff is a function defined in the set of natural numbers N={0,1,2,3,4,5,...}N = \{0, 1, 2, 3, 4, 5,...\} such that f(1)=1335f(1) = 1335 and f(n+1)=f(n)−2n+43f(n+1) = f(n)-2n+43 for all n∈Nn \in N, then his year of birth is the maximum value that f(n)f(n) can reach when nn takes values in NN. Determine the year of birth of Mary.
Back to ProblemsView on AoPS