| 罗家贵.五次完全幂的少位数三进制展开*[J].数学年刊A辑,2021,42(4):359~378 |
| 五次完全幂的少位数三进制展开* |
| Perfect Powers of Five with Few Ternary Digits |
| Received:April 10, 2020 Revised:July 23, 2021 |
| DOI：10.16205/j.cnki.cama.2021.0029 |
| 中文关键词: 丢番图方程, 三进制, 同余, 正整数解 |
| 英文关键词:Diophantine equations, 3-Adic, Congruence, Positive integer solution |
| 基金项目:国家自然科学基金(No.11871058)和四川省教育厅重大专项(No.16ZA0173) |
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| 中文摘要: |
| 本文讨论了Michael Bennett [Bennett M, Bugeaud Y, Mignotte M. Perfect powers with few binary digits and related Diophantine problem [J]. Ann Sc Norm Super Pisa Cl Sci, 2013,XII:941–953.]中提出的一类丢番图方程, 即五次完全幂的少位数三进制展开. 作者证明了丢番图方程 3a + 3b + 2 = n5, a > b > 0 有唯一的正整数解$(a,b,n)=(3,1,2). |
| 英文摘要: |
| In this paper, the authors analyze a diophantine equation raised by Michael Bennett in [Bennett, M., Bugeaud, Y., and Mignotte, M., Perfect powers with few binary digits and related Diophantine problem, Ann. Sc. Norm. Super. Pisa Cl. Sci, 2013, vol.XII, pp. 941–953.] that is pivotal in establishing that powers of five has few digits in its ternary expansion. They show that (a, b, n) = (3, 1, 2) is the only positive integer solution of Diophantine equation3a + 3b + 2 = n5, a > b > 0 |
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