Concept guide
Finite integral domain: deciding ℤ/5ℤ and ℤ/6ℤ from complete tables, then deriving invertibility from finiteness
Using complete multiplication tables, decide that ℤ/5ℤ is a finite integral domain and ℤ/6ℤ is not; then prove, as a theorem that comes after the definition, that every nonzero element of any finite integral domain is invertible, using finiteness; find all inverses in ℤ/5ℤ and explain why 2 has no inverse in ℤ/6ℤ.