Proof.
Let
![$\displaystyle P = \{ a : 1\leq a \leq n$](img94.png)
and
In the same way that we proved Lemma
3.2,
we see that the reductions modulo
![$ n$](img4.png)
of the elements of
![$ xP$](img95.png)
are exactly the same as the reductions of the elements of
![$ P$](img96.png)
.
Thus
since the products are over exactly
the same numbers modulo
![$ n$](img4.png)
.
Now cancel the
![$ a$](img13.png)
's on both sides to get
as claimed.