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Number Theory

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Sum of Legendre Symbols for a Quadratic Polynomial

NUMTH-HFWSKO

Let $p$ be an odd prime. Find the value of the sum of Legendre symbols:

$$ \sum_{x=1}^{p-1} \left(\frac{x(x+1)}p\right)= $$

A

$1$

B

$0$

C

$-1$

D

$2$

E

$-2$