Weighted complete Legendre-symbol sum

For

T = \sum_{a = 1}^{p - 1} a (\frac{a}{p})

, one has

T = 0

when

p \equiv 1 (mod 4)

, and

T \equiv 0 (mod p)

for every

p > 3

.

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 11G / c / ii / Solution

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