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

theorem Th46:
  17 divides n iff 17 divides
  value(mid(digits(n,10),2,len(digits(n,10))),10) - 5*digits(n,10).0
  proof
    reconsider p=17 as Prime by PEPIN:60;
    A1: 10*5 + 1 = p*3;
    p,10 are_coprime by EULER_1:2;
    hence thesis by Th37,A1;
  end;
