广义Pell方程Ax^2-By^2=4的通解公式 |
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引用本文: | 史保怀,李小雪. 广义Pell方程Ax^2-By^2=4的通解公式[J]. 纯粹数学与应用数学, 2014, 0(5): 441-446 |
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作者姓名: | 史保怀 李小雪 |
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作者单位: | 陕西学前师范学院数学系;西北大学数学学院; |
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基金项目: | 国家自然科学基金(11371291);陕西学前师范学院科研基金(11KJ003) |
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摘 要: | 主要运用 Lucas 数的奇偶性,讨论了当 A, B 是适合 A〉1,2-AB 且 AB 非平方数的正整数时,广义 Pell 方程的整数解(x, y),即给出了方程 Ax^2 -By^2=4适合gcd(x, y)=1的整数解(x, y)的通解公式。
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关 键 词: | 二元二次Diophantine方程 通解公式 Lucas数的奇偶性 |
The general solution formula of the generalized Pell equation Ax^2-By^2=4 |
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Affiliation: | Shi Baohuai, Li Xiaoxue (1. Department of Mathematics, Shaanxi Xuqian Normal University, Xian 710100, China; 2. School of Mathematics, Northwest University, Xian 710127, China) |
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Abstract: | The main purpose of this paper is using the parity of Lucas numbers, to discuss the integer solutions (x, y) of the equation when A, B be positive integers such that A 〉 1, 2 - AB, and AB is not a complete square, which gives a general solution formula of integer solutions (x, y) of the equation Ax^2-By^2 = 4 with gcd(x, y)=1. |
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Keywords: | binary quadratic diophantine equation general solution formula parity of Lucas number 2010 MSC |
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