Mochizuki 3-cocycle invariants for Alexander Quandles 3-cocycle formula f(x,y,z)=(x-y)^3^0 *(y-z)^3^1 *z^0 Alexander Quandle Z_3[t^1,t^-1]/(t^2+2*t+2) 6_2 [1, 1, 1, -2, 1, -2] Gcd(t^2+2*t+2,t^4-3*t^3+3*t^2-3*t+1) mod 3 =t^2+2*t+2 729 7_3 [1, 1, 1, 1, 1, 2, -1, 2] Gcd(t^2+2*t+2,2*t^4-3*t^3+3*t^2-3*t+2) mod 3 =t^2+2*t+2 729 8_8 [1, 1, 1, 2, -1, -3, 2, -3, -3] Gcd(t^2+2*t+2,2*t^4-6*t^3+9*t^2-6*t+2) mod 3 =t^2+2*t+2 729 9_14 [1, 1, 2, -1, -3, 2, -3, 4, -3, 4] Gcd(t^2+2*t+2,2*t^4-9*t^3+15*t^2-9*t+2) mod 3 =t^2+2*t+2 729 9_16 [1, 1, 1, 1, 2, 2, -1, 2, 2, 2] Gcd(t^2+2*t+2,2*t^6-5*t^5+8*t^4-9*t^3+8*t^2-5*t+2) mod 3 =t^2+2*t+2 729 9_45 [1, 1, 2, -1, 2, 1, 3, -2, 3] Gcd(t^2+2*t+2,t^4-6*t^3+9*t^2-6*t+1) mod 3 =t^2+2*t+2 729