Count all the functions
Source: VietNam Olympiad 1999, problem 6
February 6, 2004
functionmodular arithmeticalgebra solvedalgebra
Problem Statement
Let S \equal{} \{0,1,2,\ldots,1999\} and T \equal{} \{0,1,2,\ldots \}. Find all functions such that
(i) f(s) \equal{} s \forall s \in S.
(ii) f(m\plus{}n) \equal{} f(f(m)\plus{}f(n)) \forall m,n \in T.