Let f(n)(x) denote the nth iterate of function f, i.e f(1)(x)=f(x), f(n+1)(x)=f(f(n)(x)).
Let p(n) be a given polynomial with integer coefficients, which maps the positive integers into the positive integers. Is it possible that the functional equation f(n)(n)=p(n) has exactly one solution f that maps the positive integers into the positive integers?Submitted by Dávid Matolcsi and Kristóf Szabó, Budapest algebrafunctional equationpolynomial