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 Th47:
  17 divides 2|^1105-2
  proof
    255 = 17*15;
    then 2|^8,1 are_congruent_mod 17 by Lm8;
    then 2|^8|^5,1|^5 are_congruent_mod 17 by GR_CY_3:34;
    then 2|^40*2,1*2 are_congruent_mod 17 by Lm1125,INT_4:11;
    then
A1: 2|^(40+1),2 are_congruent_mod 17 by NEWTON:6;
    2|^56,1|^7 are_congruent_mod 17 by Lm1144,Lm1145,Lm1146,INT_1:15;
    then 2|^56|^19,1|^19 are_congruent_mod 17 by GR_CY_3:34;
    then 2|^1064*2|^41,1*2|^41 are_congruent_mod 17 by Lm1130,INT_4:11;
    then 2|^1105,2 are_congruent_mod 17 by A1,Lm1131,INT_1:15;
    hence thesis;
  end;
