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| 关于不定方程x3 + 27 = 139y2 |
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| 引用本文： | 熊川,罗明 .关于不定方程x3 + 27 = 139y2 [J].重庆师范大学学报(自然科学版),2012(2):47-50. |
| 作者姓名： | 熊川 罗明 |
| 作者单位： | 西南大学数学与统计学院 |
| 摘 要： | 利用Pell方程,递归数列,同余式和平方剩余几种初等方法证明了不定方程x3+27=139y2仅有整数解(-3,0),(13,±4);在证明该结论的过程中,同时证明了不定方程x3+1=417y2仅有整数解(x,y)=(-1,0),从而给出了不定方程x3+27=139y2的全部整数解。 |
| 关 键 词： | 不定方程 整数解 递归数列 |
On the Diophantine Equation x3+ 27 = 139y2 |
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| XIONG Chuan,LUO Ming .On the Diophantine Equation x3+ 27 = 139y2 [J].Journal of Chongqing Normal University:Natural Science Edition,2012(2):47-50. |
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| Authors: | XIONG Chuan LUO Ming |
| Affiliation: | (School of Mathematics and Statistics,Southwest University,Chongqing 400715,China) |
| Abstract: | By using the elementary method of recurrent sequence,congruent formula and quadratic residue,the authors prove that the diophantine equation x3+27=139y2 has only the integer solutions(x,y)=(-3,0),(13,±4).In the process of proving the conclusion,the authors also prove that the diophantine equation x3+1=417y2 has only the integer solution(x,y)=(-1,0),and then give all integer solutions of x3+27=139y2. |
| Keywords: | diophantine equation integer solution recurrent sequence |
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