reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem Th34:
  for n being positive Nat holds 3 divides (3*a+2) * 2|^(2|^n) + 1
  proof
    let n be positive Nat;
A1: 3 divides 2 * 2|^(2|^n) + 1 by Lm13;
A2: 3 divides 3*(a*2|^(2|^n));
    (3*a+2) * 2|^(2|^n) + 1 = 3*a*2|^(2|^n) + (2*2|^(2|^n) + 1);
    hence thesis by A1,A2,NAT_D:8;
  end;
