It is the Cartesian product of two affine E677 magmas.
On F_43, define
x * y = 36x + 14y + 1 mod 43.
On F_3^2, define
r * s = r + As,
where
A = [[0,1],[1,1]].
The full operation on F_43 x F_3^2 is therefore
(x,r) diamond (y,s) = (36x + 14y + 1, r + As).
The magma has 43 x 9 = 387 elements.
For the scalar component, E677 reduces to the three congruences
ab(1+b^2) = 1,
a + b^2(a^2+b) = 0,
b^2(a+1) + b + 1 = 0.
For a = 36 and b = 14 modulo 43, one has b^2 = 24, and direct substitution gives
36 x 14 x 25 = 1 mod 43,
36 + 24(36^2 + 14) = 0 mod 43,
24 x 37 + 14 + 1 = 0 mod 43.
omegaestable · 2026-07-22 04:27:37
F
43
,x∗y=36x+14y+1,
and
F
3
2
,r∗s=r+As,A=(
0
1
1
1
).
Thus the full operation is
(x,r)⋄(y,s)=(36x+14y+1,r+As),
on 43⋅9=387 elements.
omegaestable · 2026-07-22 04:28:27
omegaestable · 2026-07-22 04:27:37