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
  2|^(n+12),2|^n are_congruent_mod 65
  proof
    2|^n,2|^n are_congruent_mod 65 by INT_1:11;
    then 2|^n*2|^12,2|^n*1 are_congruent_mod 65 by Lm1107,Lm1118,INT_1:18;
    hence thesis by NEWTON:8;
  end;
