This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

1998 Poland - Second Round, 1
Tags: functional equation , function , composite function , algebra
Let $A_n = \{1,2,...,n\}$. Prove or disprove: For all integers $n \ge 2$ there exist functions $f,g : A_n \to A_n$ which satisfy $f(f(k)) = g(g(k)) = k$ for $1 \le k \le n$, and $g(f(k)) = k +1$ for $1 \le k \le n -1$.