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 Th53:
  17 divides 3|^561-3
  proof
    10000*(4304)+6720 = 17*(100*25321+60);
    then 3|^16,1 are_congruent_mod 17 by Lm1108,Lm1143,Lm1133;
    then 3|^16|^35,1|^35 are_congruent_mod 17 by GR_CY_3:34;
    then 3|^560*3|^1,1*3 are_congruent_mod 17 by Lm1136,INT_4:11;
    then 3|^(560+1),3 are_congruent_mod 17 by NEWTON:8;
    hence thesis;
  end;
