| 关于几个丢番图方程 |
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| 引用本文： | 周佐民.关于几个丢番图方程[J].高师理科学刊,1997(4). |
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| 作者姓名： | 周佐民 |
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| 作者单位： | 克山师专 |
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| 摘 要： | 本文证明了丢番图方程x4－py4＝4及x2－py4＝4（p为奇素数）无正整数解；在D＞0且不被10K＋1形素因数整除时，方程x5－1＝Dy2在x1（mod20）时反有正整数解D＝2，x＝3，y＝11．
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| 关 键 词： | 丢番图方程 方程解 |
On Several Diophantine Equations |
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| Zhou Zuomin.On Several Diophantine Equations[J].Journal of Science of Teachers＇College and University,1997(4). |
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| Authors: | Zhou Zuomin |
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| Institution: | Keshan Junior Teachers College |
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| Abstract: | In this paper, we've proved the follwing theorems:The diophantine equation x4-py4= 4, where p is an odd prime,has no integer solution ;the diophantine equation x4-pg4= 4, where p=3(mod 4) is an odd prime,has' no integer solution;let d>0,and it hasn' t any prime divisor of 10 k+1 form,then the diophantine equation x5- 1=dy2 with x 1 (mod 20) has only a positive integer solution d = 2, x = 3 and y= 11. |
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| Keywords: | Diophantine equation Solution of equation |
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