Brewer sum

The Brewer sum is given by

${\displaystyle \Lambda _{n}(a)=\sum _{x{\bmod {p}}}{\binom {D_{n+1}(x,a)}{p}}}$

where D_n is the Dickson polynomial (or "Brewer polynomial") given by

${\displaystyle D_{0}(x,a)=2,\quad D_{1}(x,a)=x,\quad D_{n+1}(x,a)=xD_{n}(x,a)-aD_{n-1}(x,a)}$

and () is the Legendre symbol.

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

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• Brewer, B. W. (1966), "On primes of the form u²+5v²", Proceedings of the American Mathematical Society, 17 (2): 502–509, doi:10.2307/2035200, ISSN 0002-9939, JSTOR 2035200, MR 0188171, Zbl 0147.29801
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