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As in Question 319254, for an odd prime $p$ and integers $c,d$ we let $$S_p(c,d):=\sum_{x=0}^{(p-1)/2}\left(\frac{x^5+cx^3+dx}p\right).$$ If $p\equiv1\pmod4$, then we obviously have \begin{align}&\...

I was hoping somebody might be able to point me to a good reference on Gaussian hypergeometric functions defined over a finite field. the reason I'm interested is that I've encountered sums of the ...