The Maximal Difference of Different Powers of an Element Modulo n
In this paper, we investigate the maximal difference of integer powers of an element modulo n. Let an denote the integer b with 1≤b≤n such that a≡bmod n for any integer a. Using the bounds for exponential sums, we obtain a lower bound of the function Hm1,m2n:=maxam1n−am2n:1≤a≤n,a,n=1, which gives n−...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8002211 |
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| _version_ | 1850178441092005888 |
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| author | Jinyun Qi Zhefeng Xu |
| author_facet | Jinyun Qi Zhefeng Xu |
| author_sort | Jinyun Qi |
| collection | DOAJ |
| description | In this paper, we investigate the maximal difference of integer powers of an element modulo n. Let an denote the integer b with 1≤b≤n such that a≡bmod n for any integer a. Using the bounds for exponential sums, we obtain a lower bound of the function Hm1,m2n:=maxam1n−am2n:1≤a≤n,a,n=1, which gives n−Hm1,m2n=On3/4+o1. |
| format | Article |
| id | doaj-art-bc1a8fdd316944c3a97de7e1ce956859 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bc1a8fdd316944c3a97de7e1ce9568592025-08-20T02:18:43ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/8002211The Maximal Difference of Different Powers of an Element Modulo nJinyun Qi0Zhefeng Xu1School of MathematicsSchool of MathematicsIn this paper, we investigate the maximal difference of integer powers of an element modulo n. Let an denote the integer b with 1≤b≤n such that a≡bmod n for any integer a. Using the bounds for exponential sums, we obtain a lower bound of the function Hm1,m2n:=maxam1n−am2n:1≤a≤n,a,n=1, which gives n−Hm1,m2n=On3/4+o1.http://dx.doi.org/10.1155/2021/8002211 |
| spellingShingle | Jinyun Qi Zhefeng Xu The Maximal Difference of Different Powers of an Element Modulo n Journal of Mathematics |
| title | The Maximal Difference of Different Powers of an Element Modulo n |
| title_full | The Maximal Difference of Different Powers of an Element Modulo n |
| title_fullStr | The Maximal Difference of Different Powers of an Element Modulo n |
| title_full_unstemmed | The Maximal Difference of Different Powers of an Element Modulo n |
| title_short | The Maximal Difference of Different Powers of an Element Modulo n |
| title_sort | maximal difference of different powers of an element modulo n |
| url | http://dx.doi.org/10.1155/2021/8002211 |
| work_keys_str_mv | AT jinyunqi themaximaldifferenceofdifferentpowersofanelementmodulon AT zhefengxu themaximaldifferenceofdifferentpowersofanelementmodulon AT jinyunqi maximaldifferenceofdifferentpowersofanelementmodulon AT zhefengxu maximaldifferenceofdifferentpowersofanelementmodulon |