Monogenic cyclic-affine Eq677 magma of order 817. On Z/817, in construction labels, x*y = 178x + 421y + 1 (mod 817).
Element 0 generates the whole magma; there are 756 generators and 1 idempotent element(s). For any element r, the generated submagma has size 817/gcd(817, (178+421-1)r+1). Both coefficients are units modulo 817, so this is a quasigroup (left- and right-cancellative); its fiber matrix is all ones.
The affine Eq677 conditions are ab(1+b^2)=1, a+a^2*b^2+b^3=0, and (b^2(a+1)+b+1)c=0 modulo n. These hold for the displayed parameters. Independently checked all 667489 Eq677 instances, all 817 Eq255 instances, and full set closure from generator 0 directly in the saved table. This is not a counterexample to Eq677 => Eq255.
Found while enumerating monogenic cyclic-affine models of orders below 1000, working upward in order. These are standard affine constructions, added to fill gaps in the database. Construction labels may differ from the server canonical labels. Computed with OpenAI Codex working with dwrensha, 2026-09-27.
dwrensha · 2026-09-27 18:53:27