Indian Mathematical Olympiad 1990 - Problem 3
Source:
August 16, 2009
functionalgebra proposedalgebra
Problem Statement
Let be a function defined on the set of non-negative integers and taking values in the same
set. Given that
(a) \displaystyle x \minus{} f(x) \equal{} 19\left[\frac{x}{19}\right] \minus{} 90\left[\frac{f(x)}{90}\right] for all non-negative integers ;
(b) ,
find the possible values that can take.
(Notation : here refers to largest integer that is , e.g. [3.1415] \equal{} 3).