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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。运给出了形如用Legendre符号和同余的性质px2-(pn±2)y2=±1(p=-1,±3(mod 8)素数)型pell方程无正整数解的6个结论。这些结论对研究狭义pell方程x2-Dy2=±1（D是非平方的正整数）起了重要作用。 |
| 关键词: pell方程 正整数解 素数 同余 |
| DOI： |
| 分类号: |
| 基金项目: |
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| On Pell Equation px2-(pn±2)y2=±1(p=-1,±3(mod 8),p is a prime factor) |
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DU Xian-cun,HUANG Mei,ZHAO Jin-e
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| Abstract: |
| The solubility of Pell equation ax3-by2=±1(a,b∈Z+，ab is a non-square positive integer)is a very meaningful question.In this paper,by applying related knowleged of Legendre sign and nature of congruence,it works out six conclusions to judge that the sets of Pell equations such as px2-(pn±2)y2=±1(p≡-1,±3（mod 8）,and p is a prime number)have not positive integer solutions.These conclusions play an important role in the research onrestricted Pell equation x2-Dy2=±1(D is a non-square positive integer) |
| Key words: Pell Equation positive integer solution prime number congruence |
