7

Part of 2006 IberoAmerican Olympiad For University Students

Problems(1)

Homomorphisms s.t. f(f(x))=f(x) - OIMU 2006 Problem 7

Source:

Consider the multiplicative group

A=\{z\in\mathbb{C}|z^{2006^k}=1, 0<k\in\mathbb{Z}\}

of all the roots of unity of degree

2006^k

for all positive integers

k

.
Find the number of homomorphisms

f:A\to A

f(f(x))=f(x)

for all elements

x\in A

trigonometrymodular arithmeticsearchcalculusintegrationalgebrafunction