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| 摘要: |
| Pell方程Ax2-By2=-+1（A,B∈Z+,AB不是完全平方数）可解性的判别是一个非常有意义的问题.本文运用Legendre符号和同余的性质等初等方法给出了形如Ax2-By2=-+1（A,B∈Z+,AB不是完全平方数）型Pell方程无正整数解的六个给论，不是完全平方数型Pell方程无正整数解的六个结论. 这些结论对我们研究狭义Pell方程x2-Dy2=-+1（D不是完全平方数)起了重要作用. |
| 关键词: Pell方程、正整数解、素数、同余、Legendre符号 |
| DOI： |
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| On Pell Equation Ax2-By2=-+1 |
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WAN Fei, DU Xian-cun
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| Abstract: |
| The solubility of Pell equation Ax2-By2=-+1（A,B∈Z+,AB is a non-square positive integer) is a very meaningful question. In this paper, It is discussed about the positive integer solutions of Pell equation Ax2-By2=-+1（A,B∈Z+,AB is a non-square positive integer) by using the elementary method of Legendre symbol and property of congruence，it works out six conclusions to judge with the sets of Pell equation x2-Dy2=-+1（D is a non-square positive integer). |
| Key words: Pell equation positive integer solution prime factor congruence Legendre symbol |
