A227628 Number of Lipschitz quaternions X such that X^2 == X (mod n).

1, 2, 14, 2, 32, 28, 58, 2, 110, 64, 134, 28, 184, 116, 448, 2, 308, 220, 382, 64, 812, 268, 554, 28, 752, 368, 974, 116, 872, 896, 994, 2, 1876, 616, 1856, 220, 1408, 764, 2576, 64, 1724, 1624, 1894, 268, 3520, 1108, 2258, 28, 2746, 1504

Offset: 1

Author

José María Grau Ribas, Jul 18 2013

Keywords

• nonn
• mult

Links

• C. J. Miguel and R. Serodio, On the Structure of Quaternion Rings over Zp, International Journal of Algebra, Vol. 5, 2011, no. 27, pp. 1313-1325.

Crossrefs

Cf. A000118, A227477, A227499.

Programs

Mathematica

cuaternios[n_] := Flatten[Table[{{ a, -b, d, -c}, {b, a, -c, -d}, {-d, c, a, -b}, {c, d, b, a}}, {a, n}, {b, n}, {c, n}, {d, n}], 3]; cuater[n_] := Length@Select[cuaternios[n], Mod[#.# - #, n] == 0*# &]; Table[cuater[n],{n,1,100}]