MathDB

1

Part of 2003 Serbia Team Selection Test

Problems(1)

factoring p(x)-x

Source:

3/14/2008
If p(x) p(x) is a polynomial, denote by pn(x) p^n(x) the polynomial p(p(...(p(x))..) p(p(...(p(x))..), where p p is iterated n n times. Prove that the polynomial p^{2003}(x)\minus{}2p^{2002}(x)\plus{}p^{2001}(x) is divisible by p(x)\minus{}x
algebrapolynomialalgebra proposed