|
%I #2 Mar 30 2012 19:00:09
%S 1,2,1,6,10,1,1,18,22,1,30,1,1,42,46,1,58,1,66,70,1,78,82,1,1,1,102,
%T 106,1,1,126,130,1,138,1,150,1,162,166,1,178,1,190,1,1,198,210,222,
%U 226,1,1,238,1,250,1,262,1,270,1,1,282,1,306,310,1,1,330,1,346,1,1,358,366,1
%N Product modulo p of the quadratic nonresidues of p, where p = prime(n).
%C a(n) == (-1)^((p-1)/2) (mod p), if p = prime(n) is odd.
%C a(n)*A163366(n) == -1 (mod prime(n)), by Wilson's theorem.
%D Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398.
%H Rahul Gupta, <a href="http://www.cse.iitd.ernet.in/~sak/courses/ant/notes/ant.pdf">Algorithmic Number Theory, Section 24.5</a>
%F a(n) = A177861(n) modulo prime(n).
%e a(1) = 1 = the empty product, because there are no quadratic nonresidues of prime(1) = 2.
%e a(4) = 6 because the quadratic nonresidues of prime(4) = 7 are 3, 5, and 6, and 3*5*6 = 90 == 6 (mod 7).
%t Table[Mod[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], -1]]], Prime[n]], {n, 1, 80}]
%Y Cf. A177861 Product of the quadratic nonresidues of prime(n), A163366 Product modulo p of the quadratic residues of p, where p = prime(n).
%K easy,nonn
%O 1,2
%A _Jonathan Sondow_, May 14 2010
|
