Let 
denote the set of the 
numbers less than and relatively
prime to 
,
where 
is the totient function. Define
 |
(1)
|
Then a theorem of Lagrange states that
 |
(2)
|
for 
an odd prime (Hardy and Wright 1979, p. 98). Actually,
this relationship holds for some composite values as well. Value for which it holds
are 
,
3, 4, 5, 6, 7, 10, 11, 13, 17, 19, 23, 29, ... (OEIS A158008).
This can be generalized as follows. Let 
be an odd prime divisor
of 
and 
the highest power which divides 
, then
 |
(3)
|
and, in particular,
 |
(4)
|
Now, if 
is even and 
is the highest power of 2 that
divides 
,
then
 |
(5)
|
and, in particular,
 |
(6)
|
