reserve a,b,c,d,x,j,k,l,m,n for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

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;
