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| 摘要: |
| 讨论不定方程x^3+27=91y^2的整数解.方法主要利用同余,递归数列,以及Pell方程的性质,给出了不定方程x^3+27=91y^2仅有整数解(-3,0),(4,+-1);推广了不定方程的研究范围,为进一步研究提供了方向. |
| 关键词: 不定方程 整数解 递归数列 同余式 |
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| On the Diophantine Equationx^3+27=91y^2 |
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TIAN Zhi-yong,LUO Ming
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| Abstract: |
| This paper discusses that the Diophantine equation x^3+27=91y^2 only has integer solutions(-3,0)and (4,±1) with the help of the congruence expression,the nature of recurrent sequences and the property of Pell equation.The research range of the Diophantine equation is extended,which reveals the direction for further research. |
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