MathDB

Let

f(x)

be a polynomial with integer coefficients. Define a sequence

a_0, a_1, \cdots

of integers such that

a_0=0

and

a_{n+1}=f(a_n)

for all

n \ge 0

. Prove that if there exists a positive integer

m

for which

a_m=0

then either

a_1=0

a_2=0

Problem Statement