MathDB

Given integer

n

, let

W_n

be the set of complex numbers of the form

re^{2qi\pi}

, where

q

is a rational number so that

q_n \in Z

and

r

is a real number. Suppose that p is a polynomial of degree

\ge 2

such that there exists a non-constant function

f : W_n \to C

so that

p(f(x))p(f(y)) = f(xy)

for all

x, y \in W_n

. If

p

is the unique monic polynomial of lowest degree for which such an

f

exists for

n = 65

, find

p(10)

Problem Statement