For prime and ,
For all , . Then we have Assume we have . Then
Consider . If is the base representation of , then for all and . We then have We want the coefficient of in . Since , we want the coefficient of .
The coefficient of each comes from the binomial expansion of , which is . Therefore we take the product of all such , and thus we have
Note that .
This is equivalent to saying that there is no term in the expansion of .