In the next theorem, we give fairly minimal conditions that imply ......
Suppose that of all such solutions, $(x,y,z)$ is one with $y$ minimal.
Define $n$ to be minimal such that $f^n(x)=y$.
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z