<p>Let P(x) be a polynomial of degree n>1 with integer coefficients, and let k be a positive integer. Consider the polynomial Q(x) = P( P ( … P(P(x)) … )), where P occurs k times. Prove that there are at most n integers t such that Q(t)=t.</p>
<p>Let P(x) be a polynomial of degree n>1 with integer coefficients, and let k be a positive integer. Consider the polynomial Q(x) = P( P ( … P(P(x)) … )), where P occurs k times. Prove that there are at most n integers t such that Q(t)=t.</p>