| 引用本文: | 杜先存，万飞，赵金娥.关于Pell方程,,是素数ax2-mqy2=±1(m∈Z+,2▕a,q≡±1(mod4)是素数)(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2012，29（10）：11-15 |
| CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435 |
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| 摘要: |
| Pell方程ax2-mqy2=±1(a，b∈Z+,a,b不是完全平方数)可解性的判断是一个非常有意义的问题，运用Legendre符号和同余的性质给出了形如ax2-mqy2=±1(m∈Z+,2▕a,q≡±1(mod4)是素数，a,b是非完全平方数)型Pell方程无正整数解的激光结论。这些结论对研究狭义Pell方程x2-Dy2=±1(D是非平方的正整数)起来重要作用。 |
| 关键词: Pell方程 正整数解 素数 同余 Legendre符号 |
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| On Pell Equation ax2-mqy2=±1(m∈Z+,2▕a,q≡±1(mod4),p is a prime factor) |
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DU Xian-cun,WAN Fei,ZHAO Jin-e
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| Abstract: |
| The discrimination of solubility of Pell equation ax2-mqy2=±1(a，b∈Z+,a,b is not a perfect square positive integer) is a very meaningful question.In this paper,by applying related knowledge of Legendre sign and nature of congruence,it works out sever conclusions that Pell equaton such as ax2-mqy2=±1(m∈Z+,2▕a,q≡±1(mod4),p is a prime factor,a,m,q is not perfect square number) has not positive integer solution.These conclusion play an important role in studying restricted Pell equation x2-Dy2=±1(D is a non-square positive integer). |
| Key words: Pell Equation positive integer solution prime factor congruence Legendre sign |
