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 Th52:
  11 divides 3|^561-3
  proof
    10*5904+8 = 11*5368;
    then 3|^10,1 are_congruent_mod 11 by Lm1113;
    then 3|^10|^56,1|^56 are_congruent_mod 11 by GR_CY_3:34;
    then 3|^560*3|^1,1*3 are_congruent_mod 11 by Lm1135,INT_4:11;
    hence thesis by Lm1137;
  end;
