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Results tagged with quadratic-residues
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user 106551
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Permutations of squares and finite fields
Let $A_q=\{x^2:x\in\mathbb{F}_q^{*}\}$.
Let $\pi^{\prime}$ be the permutation on $A_q$ defined by $$\pi^{\prime}(a_k)=a_{\pi(k)}.$$
Then
$$
\sum_{k=1}^{(q-1)/2}a_ka_{\pi(k)}=\sum_{a\in A_q}(a\pi^{\pri …
