MathDB

f (x) \ne 0 and f (x+2) = f (x-1) f (x+5) => f (x+18) = f (x)

Source: 1998 Estonia National Olympiad Final Round grade 11 p3

March 11, 2020

functionperiodicfunctional equationfunctionalalgebra

Problem Statement

A function

f

satisfies the conditions

f (x) \ne 0

and

f (x+2) = f (x-1) f (x+5)

for all real x. Show that

f (x+18) = f (x)

for any real

x