reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve r for Real;
reserve c for Complex;
reserve e1,e2,e3,e4,e5 for ExtReal;

theorem
  5 divides 2|^(2*n+1) - 2|^(n+1) + 1 iff
  not 5 divides 2|^(2*n+1) + 2|^(n+1) + 1
  proof
    n mod (3+1) = 0 or ... or n mod (3+1) = 3 by Th11;
    hence thesis by Th39,Th40;
  end;
