Multiplicative Subgrup:
Involved Vectors:
We want to prove:
Let's define the vectors by:
Taking (to visualize an overview), the objective is to define a vector such that:
By the alternating method:
So, to complete the grand-product (which is intended to be completed at ), we only need the factor in the numerator, and in the denominator.
Usign the relation:
we obtain more than these two factors:
where we have used that and , i.e., the last element of is equal to the last element of and the same happens for the first element.
In general, in the case that there will be one more factor than the rest in the definition of .
This is the reason why in Plookup .
Plookup