Fermat Number - Relationship To Constructible Polygons

Relationship To Constructible Polygons

An n-sided regular polygon can be constructed with compass and straightedge if and only if n is the product of a power of 2 and distinct Fermat primes. In other words, if and only if n is of the form n = 2kp₁p₂…p_s, where k is a nonnegative integer and the p_i are distinct Fermat primes.

A positive integer n is of the above form if and only if its totient φ(n) is a power of 2.