reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve c for Complex;

theorem Th18:
  a divides a|^s - a|^z
  proof
    a|^(s-1+1) = a|^(s-1)*a & a|^(z-1+1) = a|^(z-1)*a by NEWTON:6;
    then a|^s-a|^z = a*(a|^(s-1)-a|^(z-1));
    hence thesis;
  end;
