| 关于丢番图方程(16n)~x+(63n)~y=(65n)~z |
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| 引用本文： | 苟莎莎, 张洪.关于丢番图方程(16n)~x+(63n)~y=(65n)~z[J].西南师范大学学报(自然科学版),2015,40(4). |
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| 作者姓名： | 苟莎莎 张洪 |
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| 作者单位： | 西南大学数学与统计学院,重庆,400715 |
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| 摘 要： | 设n是正整数,运用初等方法证明了丢番图方程(16n)x+(63n)y=(65n)z仅有整数解(x,y,z)=(2,2,2),从而得到了Jesmanowicz猜想在该情形下成立.
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| 关 键 词： | Jesmanowicz猜想 丢番图方程 初等方法 |
On the Diophantine Equation (16 n)x+ (63 n)y= (65 n)z |
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| GOU Sha-sh,ZHANG Hong.On the Diophantine Equation (16 n)x+ (63 n)y= (65 n)z[J].Journal of Southwest China Normal University(Natural Science),2015,40(4). |
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| Authors: | GOU Sha-sh ZHANG Hong |
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| Abstract: | Let n be a positive integer .In this paper ,in the elementary methods ,the author show s that the Diophantine equation (16n)x+ (63n)y= (65n)z has no solution in positive integers other than (x ,y ,z)=(2 ,2 ,2) .The result is still the confirmation of Jesmanowicz's conjecture . |
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