| 摘要: |
| 不定方程是数论研究的一个重要分支，不仅其自身发展活跃，而且离散数学的各个领域也有重要的应用，对于解决现实问题有着重要的作用.主要利用pell方程、递归数列、同余式和平方剩余几种初等方法，针对D=73时，不定方程x3±64=Dy2的解进行讨论，证明了不定方程x3±64=73y2仅有整数解(x,y)=(4,0) |
| 关键词: 不定方程 整数解 递归数列 同余式 |
| DOI： |
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| On Diophantine Equation x3±64=73y2 |
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ZHENG Ai lin
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| Abstract: |
| The Diophantine equation is an important branch of number theory research, not only itself development is active but also it has important application in discrete mathematics, as a result, it plays an important role in solving real problems. Many scholars at home and abroad extensively and deeply study it for many years. By the elementary methods such as pell equation, recurrent sequence, congruence expression, and square residue, the solution to the Diophantine equation x3±64=Dy2 is discussed when D=73, and this paper proves that the Diophantine equation x3±64=73y2 only has integer solution (x,y)=(4,0). |
| Key words: Diophantine equation integer solution recurrent sequence congruence expression |
