| 丢番图方程3n+px2=yp |
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| 引用本文： | 潘家宇. 丢番图方程3n+px2=yp[J]. 河南科学, 2011, 29(12): 1416-1420 |
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| 作者姓名： | 潘家宇 |
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| 作者单位： | 河南工业大学数学系,郑州,450000 |
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| 基金项目： | Research Project of Henan University of Technology （2006XJC038） |
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| 摘 要： | 讨论了丢番图方程3n+px2=yp(x,y,n∈N；p是奇素数)的可解性,得到以下结果:(1)当p=3时,方程的所有解为(x,y,n)=(46·33t+1,13·32t+1,6t+7),(10·33t+1,7·32t+1,6t+8).(2)当p=1(mod 24)时,方程没有解.
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| 关 键 词： | 丢番图方程 二次数域 类数 |
The Diophantine Equation 3n+px2=yp |
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| Pan Jiayu. The Diophantine Equation 3n+px2=yp[J]. Henan Science, 2011, 29(12): 1416-1420 |
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| Authors: | Pan Jiayu |
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| Affiliation: | Pan Jiayu (Department of Mathematics, Henan University of Technology, Zhengzhou 450000, China) |
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| Abstract: | The solvability of Diophanine equation 3n＋px2=y^p was investigated in this paper. If p =3, the equation has only solution （x,y,n）=（46·3^3t＋1,13·3^2t＋1,6t＋7）,（10·3^3t＋1,7·3^2t＋1,6t＋8）.If p =1 （mod 24）, then the equation has no solution. |
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| Keywords: | Diophanine equation quadratic number field class number |
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