reserve a,b,c,k,m,n for Nat;
reserve p for Prime;

theorem Th19:
  a divides b implies n|^a - 1 divides n|^b - 1
  proof
    given m being Nat such that
A1: b = a*m;
    n|^a - 1 divides n|^a|^m - 1|^m by NEWTON01:33;
    hence thesis by A1,NEWTON:9;
  end;
