reserve i,s,t,m,n,k for Nat,
        c,d,e for Element of NAT,
        fn for FinSequence of NAT,
        x,y for Integer;
reserve p for Prime;

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;
