| 关于丢番图方程ax~4+by~4=cz~2 |
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| 引用本文： | 佟瑞洲.关于丢番图方程ax~4+by~4=cz~2[J].宝鸡文理学院学报(自然科学版),2011,31(2):1-3,10. |
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| 作者姓名： | 佟瑞洲 |
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| 作者单位： | 朝阳师范高等专科学校，辽宁朝阳,122000 |
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| 基金项目： | 辽宁省教育厅科研立项课题(20401232) |
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| 摘 要： | 目的对某类特殊的正整数a,b,c,寻找给出丢番图方程ax4+by4=cz2的全部正整数解的方法。方法利用初等方法把方程ax4+by4=cz2化为方程x2+my2=z2,给出方程ax4+by4=cz2的全部正整数解。结果给出了当(a,b,c)=(5,3,2)时方程ax4+by4=cz2的全部正整数解。结论利用上述方法可以解决一类方程ax4+by4=cz2的求解问题,从而拓展了Mordell等人关于ax4+by4=cz2的结果。
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| 关 键 词： | 丢番图方程 正整数解 两两互素 |
On the Diophantine equation ax~4+by~4=cz~2 |
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| TONG Rui-zhou.On the Diophantine equation ax~4+by~4=cz~2[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2011,31(2):1-3,10. |
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| Authors: | TONG Rui-zhou |
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| Institution: | TONG Rui-zhou(Chaoyang Teachers College,Chaoyang 122000,Liaoning,China) |
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| Abstract: | Aim To find the method of all positive integer solutions of Diophantine equation ax4+by4=cz2 for some special positive integers a,b and c.Methods ax4+by4=cz2 is changed into x2+my2=z2 by using elementary methods,then all positive integer solutions of Diophantine equation ax4+by4=cz2 are given.Results The all positive integer solutions of Diophantine equation ax4+by4=cz2 are given when(a,b,c)=(5,3,2).Conclusion The foregoing method may be used to solve a class of equations such as ax4+by4=cz2 and the results... |
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| Keywords: | Diophantine equation positive integer solution prime to each other |
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