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 Th57:
  5 divides 3|^1105-3
  proof
    3|^4|^276,1|^276 are_congruent_mod 5 by Lm1142,GR_CY_3:34;
    then 3|^1104*3|^1,1*3 are_congruent_mod 5 by Lm1138,INT_4:11;
    hence thesis by Lm1139;
  end;
