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

theorem Th82:
  97 divides n iff 97 divides
  value(mid(digits(n,10),2,len(digits(n,10))),10) - 29*digits(n,10).0
  proof
    reconsider p=97 as Prime by Th35;
    A1: 10*29 + 1 = p*3;
    p,10 are_coprime by EULER_1:2;
    hence thesis by Th37,A1;
  end;
