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 ci is a non-zero integer. Define a sequence {an} 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 a2008=0 functionalgebrapolynomialinductionalgebra proposed