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Cyclic p-roots of prime lengths p(n).
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%I #10 Sep 26 2024 02:58:19

%S 2,6,70,924,184756,2704156,601080390,9075135300,2104098963720,

%T 7648690600760440,118264581564861424,442512540276836779204,

%U 107507208733336176461620,1678910486211891090247320,410795449442059149332177040

%N Cyclic p-roots of prime lengths p(n).

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

%H Uffe Haagerup, <a href="http://arXiv.org/abs/0803.2629">Cyclic p-roots of prime lengths p and related complex Hadamard matrices</a>, arXiv:0803.2629 Mar 19, 2008.

%F a(n) = (2*p_n - 2)!/(p_n - 1)!^2 where p_n = prime(n) = A000040(n).

%F a(n) = A000142(2*A000040(n)-2)/((A000142(A000040(n)-1))^2).

%Y Cf. A000040, A000142.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 18 2008