关于Diophantine方程x~3-5~3=2Dy~2的整数解 |
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引用本文: | 廖军,;杜先存.关于Diophantine方程x~3-5~3=2Dy~2的整数解[J].长沙大学学报,2014(2):7-8. |
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作者姓名: | 廖军 ;杜先存 |
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作者单位: | [1]文山学院数学学院,云南文山663000; [2]红河学院教师教育学院,云南蒙自661199 |
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基金项目: | 文山学院重点学科数学建设项目(批准号:12WSXK01) |
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摘 要: | 设D为奇素数,运用平方剩余、同余式、乐让德符号的性质等初等方法得出了Diophantine方程x3-53=2Dy2无x≠0(mod 5)的正整数解的两个充分条件.
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关 键 词: | Diophantine方程 奇素数 同余 平方剩余 正整数解 乐让德符号 |
On the Solution of the Diophantine Equation x^3-5^3=2Dy^2 |
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Institution: | LIAO Jun, DU Xiancun ( 1. College of Mathematics, Wenshan University, Wenshan Yunnan 663000, China; 2. Teachers' Educational College, Honghe University, Mengzi Yunnan 661199, China) |
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Abstract: | Let D be an odd prime. By using quadratic residue, congruent formula and legendre symbol, two sufficient conditions are obtained when the Diophantine equation x^3-5^3=2Dy^2 has no integer solutions with x≠0( mod 5). |
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Keywords: | Diophantine equation odd prime congruence quadratic residue positive integer solution legendre symbol |
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