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Since there are 31 combinations of anywhere from one to five Fermat primes, there are 31 known constructible polygons with an odd number of sides.
The next twenty-eight Fermat numbers, ''F''<sub>5</sub> through ''F''<sub>32</sub>, are known to be composite.<ref>[http://www.prothsearch.com/fermat.html
and complete factoring status] by Wilfrid Keller.</ref>
Thus a regular ''n''-gon is constructible if
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