MathCastle
Groups and FieldsHardGroups and the Group Axioms

Groups and the Group Axioms · Hard problem

On Z7={0,1,…,6}\mathbb{Z}_7=\{0,1,\ldots,6\} define a∗b=(a−b) mod 7a*b=(a-b)\bmod 7. For how many of the 343343 ordered triples (a,b,c)∈Z73(a,b,c)\in\mathbb{Z}_7^3 does (a∗b)∗c=a∗(b∗c)(a*b)*c=a*(b*c) hold?