| 不定方程x^2-py^2=z^2的正整数解 |
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| 引用本文： | 管训贵.不定方程x^2-py^2=z^2的正整数解[J].张家口农专学报,2009(5):5-7. |
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| 作者姓名： | 管训贵 |
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| 作者单位： | 泰州师范高等专科学校,江苏泰州225300 |
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| 摘 要： | 研究了一类不定方程求正整数解的问题.借助一个引理,推导并证明了不定方程x^2-py^2=z^2（p为奇素数）正整数解的一般公式.不定方程x^2-py^2=z^2（p为奇素数）满足（x,y）=1的一切正整数解可表示为x=12（a^2＋pb^2）,y=ab,z=│12a2-pb2│,这里a〉0,b〉0,a,b都是奇数,p a;或x=a^2＋pb^2,y=2ab,z=│a2-pb2│,这里a〉0,b〉0,a,b一奇一偶,p a.
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| 关 键 词： | 不定方程 正整数解 模p同余 素数 奇数 偶数 |
Positive Integral Solution of Indeterminate Equation x^2-py^2=z^2 |
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| Authors: | GUAN Xun-gui |
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| Institution: | GUAN Xun-gui (Taizhou Normal College, Taizhou 225300, Jiangsu, China) |
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| Abstract: | The problem of positive integral solution of a kind of indeterminate equation is studied.With a Lemma,the general formulas of positive integral solution of the indeterminate equation x^2-py^2=z^2（let p〉2 be a prime number） are deduced and proved.With（x,y）=1,we have x=1/2（a^2＋pb^2）,y=ab,z=1/2│a^2-pb^2│,where a〉0,b〉0,a is odd and b is odd,pa;or x=a^2＋pb^2,y=2ab,z=│a^2-pb^2,where a〉0,b〉0,a is even and b is odd,or a is odd and b is even,pa. |
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| Keywords: | indeterminate equation positive integral solution congruence modulo p prime number odd even |
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