The possibility of solving the problem of the elementary division of a circumference into equal parts was known to the ancients for the cases

n = 2p, n = 3, n = 5, and their products.

Gauss in his Disquisitiones Arithmeticae proved the possibility of solving the problem by quadratics, and therefore geometrically with ruler and the compass, for all the prime numbers of the series

n = 22p + 1.