MathDB

Let f(x) \equal{} c_m x^m \plus{} c_{m\minus{}1} x^{m\minus{}1} \plus{}...\plus{} c_1 x \plus{} c_0, where each

c_i

is a non-zero integer. Define a sequence

\{ a_n \}

by a_1 \equal{} 0 and a_{n\plus{}1} \equal{} f(a_n) for all positive integers

n

. (a) Let

i

and

j

be positive integers with

i<j

. Show that a_{j\plus{}1} \minus{} a_j is a multiple of a_{i\plus{}1} \minus{} a_i. (b) Show that

a_{2008} \neq 0

Problem Statement