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

theorem
  14,35 satisfy_Sierpinski_problem_35
  proof
    1260 = 6*210;
    hence 14*(14+1) divides 35*(35+1);
    35 = 2*14+7;
    hence not 14 divides 35 by NAT_4:9;
    35 = 2*15+5;
    hence not 14+1 divides 35 by NAT_4:9;
    36 = 2*14+8;
    hence not 14 divides 35+1 by NAT_4:9;
    36 = 2*15+6;
    hence not 14+1 divides 35+1 by NAT_4:9;
  end;
