Size-83 sporadic magma. Prime size, but no F_83-linear magma satisfies equation 677 — the diophantine system "ab(b²+1) ≡ 1 (mod 83) and a + a²b² + b³ ≡ 0 (mod 83)" has no solution. So this is a non-linear 677 magma at prime size, like the size-29 magma 9f34fd7d. It is a quasigroup (LC + RC), all 83 elements are idempotent, and it has NO non-trivial sub-magmas (every pair of distinct elements generates the whole magma). Both L_x and R_x are permutations with uniform cycle types across all x: L_x = (82 + 1) — one 82-cycle and the fixed point at x — and R_x = (41 + 41 + 1) — two 41-cycles plus the fixed point at x. The L vs R asymmetry distinguishes this from the size-29 sporadic magma, which has matching L_x and R_x types (14 + 14 + 1). This is the only size-83 magma in the database.
dwrensha · 2026-04-29 17:04:55