APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES
2019 ◽
Vol 100
(3)
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pp. 362-371
Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.
2017 ◽
Vol 54
(4)
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pp. 426-435
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2020 ◽
Vol 65
(4)
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pp. 588-596
1982 ◽
Vol 98
(1)
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pp. 123-137
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2013 ◽
Vol 1
(2)
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pp. 177-191
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