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 = 2kp1p2ps, where k is a nonnegative integer and the pi 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.

Read more about this topic:  Fermat Number

Famous quotes containing the words relationship to and/or relationship:

    Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.
    Friedrich Nietzsche (1844–1900)

    Sisters is probably the most competitive relationship within the family, but once the sisters are grown, it becomes the strongest relationship.
    Margaret Mead (1901–1978)