A236553 Number of involutions in the quaternion ring over Z/nZ with i^2=j^2=1.

1, 8, 14, 64, 32, 112, 58, 288, 110, 256, 134, 896, 184, 464, 448, 1056, 308, 880, 382, 2048, 812, 1072, 554, 4032, 752, 1472, 974, 3712, 872, 3584, 994, 4128, 1876, 2464, 1856, 7040, 1408, 3056, 2576, 9216, 1724, 6496, 1894, 8576, 3520, 4432, 2258, 14784, 2746

Offset: 1

Author

José María Grau Ribas, Jan 28 2014

Keywords

• nonn
• mult

Comments

Number of solutions modulo n of the equation system:

a^2 - b^2 + c^2 + d^2 = 1

2ab = 0

2ac = 0

2ad = 0.

Crossrefs

Cf. A236554, A227867.

Programs

Mathematica

invo11[n_] :=  Length@Reduce[a^2 - b^2 + c^2 + d^2 ==1 && 2 a b== 0 && 2 a c == 0 && 2 a  d == 0, Modulus -> n];Table[invo11[n],{n,1,44}]