reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th39:
  17 divides 2|^561-2
  proof
    2|^56,1|^7 are_congruent_mod 17 by Lm1144,Lm1145,Lm1146,INT_1:15;
    then 2|^56|^10,1|^10 are_congruent_mod 17 by GR_CY_3:34;
    then 2|^560*2|^1,1*2 are_congruent_mod 17 by Lm1120,INT_4:11;
    then 2|^(560+1),2 are_congruent_mod 17 by NEWTON:8;
    hence thesis;
  end;
