MathDB

Let

t = (a, b, c)

, and let us define

f^1 (t) = (a + b, b + c, c + a)

and

f^k (t) = f^{k-1}(f^1(t))

for all

k > 1

. Furthermore, a permutation of

t

has the same elements, just in a different order (e.g.,

(b, c, a)

). If

f^{2013}(s)

is a permutation of

s

for some

s = (k, m, n)

, where

k, m

, and

n

are integers such that

|k|, |m|, |n|\le 10

, how many possible values of

s

are there?

Problem Statement