theorem
  n>1 & i,n are_coprime implies order(i,n) divides Euler n
proof
  assume
  A1:n>1 & i,n are_coprime;
  (i |^ Euler n) mod n = 1 by Th5,A1,EULER_2:18;
  hence thesis by A1,PEPIN:47;
end;
