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In this paper it is proved, that for every prime number p, the set of cyclicp-roots in C^p is finite. Moreover the number of cyclic p-roots counted withmultiplicity is equal to (2p-2)!/(p-1)!^2. In particular, the number of complexcirculant Hadamard matrices of size p, with diagonal entries equal to 1, isless or equal to (2p-2)!/(p-1)!^2.

Cyclic p-roots of prime lengths p and related complex Hadamard matrices