| 方程xy+yz+zx=n的正整数解 |
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| 引用本文： | 袁平之. 方程xy+yz+zx=n的正整数解[J]. 数学学报, 2000, 43(3): 391-398. DOI: cnki:ISSN:0583-1431.0.2000-03-001 |
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| 作者姓名： | 袁平之 |
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| 作者单位： | 长沙铁道学院数理力学系!湖南长沙410075 |
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| 摘 要： | 本文用 Ｓｉｅｇｅｌ－Ｔａｔｕｚａｗａ定理证明了：当ｎ＞１．２×１０~１１时，至多有两个正 整数ｎ。使方程ｘｕ＋ｙｚ＋ｚｘ＝ｎ无适合（ｘ，ｙ，ｚ）＝１且０＜ｘ＜ｙ＜ｚ的解（ｘ，ｙ，ｚ）， 并给出类数为２的二次域与多项式表素数的一个结果．
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| 关 键 词： | 二元二次原型 类数 正整数解 多项式 |
On the Positive Integer Solutions of the Equation xy+yz+zx=n |
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| YUAN Ping-zhi. On the Positive Integer Solutions of the Equation xy+yz+zx=n[J]. Acta Mathematica Sinica, 2000, 43(3): 391-398. DOI: cnki:ISSN:0583-1431.0.2000-03-001 |
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| Authors: | YUAN Ping-zhi |
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| Affiliation: | YUAN Ping-zhi (Department of Mathematics and Mechanics, Changsha Railway University, Changsha 410075, P. R. China) |
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| Abstract: | In this paper, by using Siegel-Tatuzawa Theorem, we prove that: if n > 1.2 × 10~11, then there is at most two positive integers n such that xy+yz+zx=n has no solutions with (x,y,z) = 1 and 0 < x < y < z. And we obtain a result related to the quadratic fields of class number 2 and the polynomials denoting primes. |
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| Keywords: | Binary quadratic primitive forms Class numbers Positive integer solutions Polynomial |
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