| 关于方程xy+yz+zx=n的正整数解 |
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| 引用本文： | 陈锡庚,乐茂华. 关于方程xy+yz+zx=n的正整数解[J]. 数学学报, 1998, 41(3): 577-582. DOI: cnki:ISSN:0583-1431.0.1998-03-021 |
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| 作者姓名： | 陈锡庚 乐茂华 |
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| 作者单位： | 茂名教育学院数学系(陈锡庚)，湛江师范学院数学系(乐茂华) |
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| 基金项目： | 国家自然科学基金,广东省自然科学基金 |
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| 摘 要： | 本文在广义Ｒｉｅｍａｎｎ猜想成立的条件下证明了：当且仅当正整数ｎ＝１，２，４，６，１０，１８，２２，３０，４２，５８，７０，７８，１０２，１３０，１９０，２１０，３３０，４６２时，方程ｘｙ＋ｙｚ＋ｚｘ＝ｎ无正整数解（ｘ，ｙ，ｚ）．
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| 关 键 词： | 三元二次丢番图方程，正整数解，二元二次原型，类数，广义Riemann猜想 |
| 收稿时间： | 1997-04-07 |
| 修稿时间： | 1997-10-17 |
On the Positive Integer Solutions of the Equation xy+yz+zx=n |
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| Chen Xigeng. On the Positive Integer Solutions of the Equation xy+yz+zx=n[J]. Acta Mathematica Sinica, 1998, 41(3): 577-582. DOI: cnki:ISSN:0583-1431.0.1998-03-021 |
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| Authors: | Chen Xigeng |
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| Affiliation: | Chen Xigeng (Department of Mathematics, Maoming Educational College, Maoming 525000, China) Le Maohua (Department of Mathematics, Zhanjiang Teachers College, Zhanjiang 524048, China) |
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| Abstract: | Let n be a positive integer. In this paper, under the assumption of the generalized Riemann conjecture, we prove that if and only if n =1,2,4,6,10,18,22,30,42,58, 70,78,102,130,190,210,330,462, then the equation xy yz zx=n has no positive integer solution (x,y,z) . |
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| Keywords: | Ternary quadratic diophantine equation Positive integer solution Binary quadratic primitive form Class number Generalized Riemann conjecture |
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