Question 12
Let $X$ denote the set of all triples $(a, b, c)$ of integers. Define a function $f: X \rightarrow X$ by
$$
f(a, b, c) = (a + b + c, ab + bc + ca, abc)
$$
Find all triples $(a, b, c)$ in $X$ such that $f(f(a, b, c)) = (a, b, c)$.
$$
f(a, b, c) = (a + b + c, ab + bc + ca, abc)
$$
Find all triples $(a, b, c)$ in $X$ such that $f(f(a, b, c)) = (a, b, c)$.