theorem Th19:
  n>0 implies t*z divides (t-z)|^n - (t|^n + (-z)|^n)
  proof
    n>0 implies t*(-z) divides (t+(-z))|^n - (t|^n + (-z)|^n) by Th17; then
    n>0 implies -(t*z) divides (t+(-z))|^n - (t|^n + (-z)|^n);
    hence thesis by INT_2:10;
  end;
