| 双曲丢番图方程正整数解数的估计及其应用 |
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| 引用本文： | 王兴波. 双曲丢番图方程正整数解数的估计及其应用[J]. 佛山科学技术学院学报(自然科学版), 2014, 0(3): 10-14 |
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| 作者姓名： | 王兴波 |
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| 作者单位： | 佛山科学技术学院机电系,广东佛山528000 |
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| 基金项目： | 国家星火计划项目（2013GA780052）;广东省工业攻关项目（20128010600018）;广东省数控一代机械产品创新应用示范工程专项资金项目（20128011300068）;佛山市科技发展专项资金项目（2011AA100021）;佛山市产学研项目（2012HC10013I）;佛山科技创新平台资助项目（2013AG10007）;禅城区产学研项目（201281011,201381018）;禅城区科技计划项目（2011A1025,2013A1021） |
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| 摘 要： | 通过对双曲丢番图方程实施等价变换，逐步剖析、细化了方程的求解并给出了解的解析结构与正整数解数的一个估计。还证明了孪生素数的存在性问题等价于求解一类双曲丢番图方程正整数的问题。
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| 关 键 词： | 初等数论 丢番图方程 正整数解 孪生素数 |
Evaluation and application of the number of positive integral solutions of a hyperbolic Diophantine equation |
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| WANG Xing-bo. Evaluation and application of the number of positive integral solutions of a hyperbolic Diophantine equation[J]. Journal of Foshan University(Natural Science Edition), 2014, 0(3): 10-14 |
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| Authors: | WANG Xing-bo |
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| Affiliation: | WANG Xing-bo (Department of Mechatronics, Foshan University, Foshan 528000 ,China) |
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| Abstract: | By an equivalent transformation on a hyperbolic Diophantine equation, the paper makes a detail analysis on process of solving the equation and presents an analytic form of the equation＇s solutions as well as an evaluation on the number of the equation＇s positive integral solutions. The paper also proves an equivalent relation between the existence of the twin primes and the solution of a class of hyperbolic Diophantine equations. |
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| Keywords: | elementary number theory Diophantine equations positive integra solutions twin primes |
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