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 or a+b divides a|^n-b|^n
  proof
    per cases;
    suppose n is odd;
      then ex k be Nat st n=2*k+1 by ABIAN:9;
      hence thesis by Th34;
    end;
    suppose n is even;
      then consider m be Nat such that
      A2: n = 2*m;
      A3: a+b divides a|^2 - b|^2 by Lm44;
      a|^2-b|^2 divides a|^(2*m) - b|^(2*m) by Th33;
      hence thesis by A2,A3,INT_2:9;
    end;
  end;
