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 Th43:
  43 divides 2|^645-2
  proof
A1: 2|^(7+7) = 2|^7*2|^7 by NEWTON:8;
    128*128-1 = 43*381;
    then 2|^14,1 are_congruent_mod 43 by A1,Lm7;
    then 2|^14|^46,1|^46 are_congruent_mod 43 by GR_CY_3:34;
    then 2|^644*2|^1,1*2 are_congruent_mod 43 by Lm1127,INT_4:11;
    hence thesis by Lm1126;
  end;
