OFFSET
1,2
COMMENTS
A quaternion q = a + bi + cj + dk is congruent to 1 (mod n) iff a == 1 (mod n) and b == c == d == 0 (mod n).
LINKS
Wikipedia, Hurwitz quaternion.
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]; invo[n_] := invo[n] = Length@Select[cuaternios[n], Mod[#.# - IdentityMatrix[4], n] == 0*# &]; Table[invo[n], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
José María Grau Ribas, Nov 02 2013
EXTENSIONS
More terms from Amiram Eldar, May 06 2024
STATUS
approved