A177861 Product of the quadratic nonresidues of prime(n).

1, 2, 6, 90, 6720, 36960, 11642400, 283046400, 2412984420000, 1140422816332800, 1226781977195174400, 1863152400854384640000, 5988092802221559085056000, 112886540292742916603904000, 158983195607776600998537600000000

Offset: 1

Author

Jonathan Sondow, May 14 2010

Keywords

• easy
• nonn

Comments

a(n) == (-1)^((p-1)/2) (mod p), if p = prime(n) is odd.

Examples

			The quadratic nonresidues of prime(4) = 7 are 3, 5, and 6, so a(4) = 3*5*6 = 90.
		

References

• Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398.

Links

• Rahul Gupta, Algorithmic Number Theory, Section 24.5

Crossrefs

A125615 Sum of the quadratic nonresidues of prime(n), A177860 Product of the quadratic residues of prime(n), A177863 Product of the quadratic nonresidues of prime(n) modulo prime(n).

Programs

Mathematica

Table[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], -1]]], {n, 1, 16}]

Formula

a(n) = (p-1)!/A177860(n), where p = prime(n).