reserve n,k,b for Nat, i for Integer;

theorem Th68:
  61 divides n iff 61 divides
  value(mid(digits(n,10),2,len(digits(n,10))),10) - 6*digits(n,10).0
  proof
    reconsider p=61 as Prime by Th29;
    A1: 10*6 + 1 = p*1;
    p,10 are_coprime by EULER_1:2;
    hence thesis by Th37,A1;
  end;
