| 混和幂的丢番图不等式(Ⅱ) |
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| 引用本文： | 余红兵.混和幂的丢番图不等式(Ⅱ)[J].数学学报,1994,37(3):324-331. |
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| 作者姓名： | 余红兵 |
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| 作者单位： | 中国科学技术大学数学系!合肥230026 |
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| 基金项目： | 国家自然科学基金资助项目． |
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| 摘 要： | 本文证明了下面的 定理设λ１，…，λ７为非零实数，其中至少有两个之比为无理数，则对任意实数κ及０＜σ＜１／３６不等式有无穷乡组整数解（ｘ１，…，ｘ７）．这是陆鸣皋教授的一个结果对丢番图不等式的类似．
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| 关 键 词： | 丢番图不等式 混和幂 高次幂和 |
| 收稿时间： | 1991-12-23 |
Diophantine Inequalities with Mixed Powers (Ⅱ) |
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| Yu Hongbing.Diophantine Inequalities with Mixed Powers (Ⅱ)[J].Acta Mathematica Sinica,1994,37(3):324-331. |
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| Authors: | Yu Hongbing |
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| Institution: | Yu Hongbing (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) |
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| Abstract: | In the present paper, we consider the analogue of professor Lu Ming-gap's theorem on sums of mixed powers for Diophantine inequalities. More precisely we have the following result. Theorem Suppose that λ１，…，λ７ are non-zero real numbers not all in rational ratio. Then for any real number K and σ < 1/36, the inequality has infinitely many solutions in integers. |
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| Keywords: | Diophantine inequality mixed powers sums of higher powers |
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