reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th73:
  3|^n - 2|^m = 1 implies n = m = 1 or n = 2 & m = 3
  proof
    per cases;
    suppose n is odd;
      hence thesis by Th71;
    end;
    suppose n is even;
      hence thesis by Th72;
    end;
  end;
