MathDB
f (2016)=? f(ab) = f (a) + f (b), f(10) = 0, f(a) = 0 when unit digit of a is 7

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist F3 day2 (F= Functions)

September 24, 2021
Digitsfunctional equationfunctionalalgebra

Problem Statement

Let f:Z+→Z+∪{0}f: Z^+ \to Z^+ \cup \{0\} a function that meets the following conditions: a) f(ab)=f(a)+f(b)f (a b) = f (a) + f (b), b) f(a)=0f (a) = 0 provided that the digits of the unit of aa are 77, c) f(10)=0f (10) = 0. Find f(2016).f (2016).
Back to ProblemsView on AoPS