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## Constructible polygons

A constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not.

• Prove that, a regular $n-gon$ can be constructed with compass and straightedge if $n$ is the product of a power of $2$ and any number of distinct Fermat primes.

• Prove that the above condition is also necessary.

Source: folklore

Hint:

See http://en.wikipedia.org/wiki/Constructible_polygon

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