Let $p$ be an odd prime. For any integer $k$, define $S(k,p) = \sum^{p}_{x=1}(\frac{x(x+k)}{p})$.
(i) Show that S(0,$p$) = $p$-1
(ii) Show that if p does not divide k then $S(k,p) = S(1,p)$
(iii) Conclude that if p does not divide k then $S(k,p) = -1$
Been struggling with this question for a couple of days with no progress.