Competition problem — Number theory

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Number theory Difficulty 6.0 AIME, harder Prove it

25. 设 $p, d, n_{1}^{\prime}$ 由第 20 题给出, $2 \nmid d$ . 证明:
$n_{1}^{\prime} \equiv \sum_{1 \leqslant j<p / 2}\left[\frac{2 j d}{p}\right](\bmod 2)$

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.