Lucas's theorem states that if 
be a squarefree integer
and 
a cyclotomic polynomial, then
 |
(1)
|
where 
and 
are integer polynomials of degree 
and 
, respectively. This identity can be expressed as
 |
(2)
|
with 
and 
symmetric polynomials. The following table gives
the first few 
and 
s
(Riesel 1994, pp. 443-456).
 |  |  |
| 2 |  | 1 |
| 3 |  | 1 |
| 5 |  |  |
| 6 |  |  |
| 7 |  |  |
| 10 |  |  |
