MathDB

3

Part of 2002 Czech-Polish-Slovak Match

Problems(1)

How many functions satisfy f^(4)(x)+x=n+1?

Source: Czech-Polish-Slovak 2002 Q3

4/28/2013
Let S={1,2,⋯ ,n},n∈NS = \{1, 2, \cdots , n\}, n \in N. Find the number of functions f:S→Sf : S \to S with the property that x+f(f(f(f(x))))=n+1x + f(f(f(f(x)))) = n + 1 for all x∈Sx \in S?
functionalgebra unsolvedalgebra