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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

Answers

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Hint:

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