APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES
| Autor: | Hai Liang Wu, Li Yuan Wang |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. 100:362-371 |
| ISSN: | 1755-1633 0004-9727 |
| Popis: | 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 $p$. |
| Databáze: | OpenAIRE |
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