theorem
  a+b divides a|^n - b|^n implies
    a+b divides a|^(n+1) + b|^(n+1)
  proof
    assume a+b divides a|^n - b|^n; then
    a+b divides a*(a|^n+0) + b*(b|^n+0) by Th31; then
    a+b divides a|^(n+1) + b*b|^n by NEWTON:6;
    hence thesis by NEWTON:6;
  end;
