Competition problem — Number theory

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Number theory Difficulty 5.8 AIME, harder Prove it

8. Let $p$ be an odd prime, $(k, p)=1$ . Prove:
$\sum_{j=0}^{p-1}\left(\frac{j(j+k)}{p}\right)=-1$

Solution

8. Exercise 6 of Chapter 4, Question 33.

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