If 
,
then 
.
The converse is also true.
If ,
then .
The converse is also true.
If 
is given by
then a multiplication by 
turns every 
into 
; and also, since
we have (with 
),
For the converse, just follow the proof backwards.
The condition 
means than is odd, and
for some 
; the representation of a number 
that is congruent to 
modulo 
can be reduced
(via this proposition) to the representation of 
.