MathDB

if f(x +19)>=f (x) + 19 and f (x + 94)<= f (x) + 94 then f (x + 1) = f (x) + 1

Source: Austrian - Polish 1994 APMC

May 3, 2020

functionalFunctional inequalityfunctional equationalgebra

Problem Statement

A function

f: R \to R

satisfies the conditions:

f (x + 19) \le f (x) + 19

and

f (x + 94) \ge f (x) + 94

for all

x \in R

. Prove that

f (x + 1) = f (x) + 1

for all

x \in R