numbers of functions
Source: Vietnam NMO 1997, Problem 3
September 5, 2008
functionnumber theoryrelatively primealgebra proposedalgebra
Problem Statement
Find the number of functions which satisfying:
(i) f(1) \equal{} 1
(ii) f(n)f(n \plus{} 2) \equal{} f^2(n \plus{} 1) \plus{} 1997 for every natural numbers n.