Brewer sum explained

In mathematics, Brewer sums are finite character sum introduced by related to Jacobsthal sums.

Definition

The Brewer sum is given by

Λ _{n(a)} = \sum _{x\bmod} \binom{D _{n+1} (x,a)}{p} where D_n is the Dickson polynomial (or "Brewer polynomial") given by D _{0} (x,a) =2 , D _{1(x,a)=x,} D _{n+1} (x,a) = xD _{n(x,a)-aD} _{n-1} (x,a) and is the Legendre symbol.

The Brewer sum is zero when n is coprime to q²−1.