引用本文: | 曹瑞, 罗明.关于不定方程x 3±1=1 379y 2(J/M/D/N,J:杂志,M:书,D:论文,N:报纸).期刊名称,2020,37(4):118-122 |
| CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435 |
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关于不定方程x 3±1=1 379y 2 |
曹瑞, 罗明
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重庆师范大学 数学科学学院,重庆 401331
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摘要: |
关于x3±1=Dy2(D>0)型不定方程的解法还没有一般性的结论;研究D=1 379时不定方程x3±1=Dy2的可解性问题,利用同余理论、递归序列、平方剩余以及Pell方程解的性质证明了不定方程x3+1=1 379y2仅有整数解(x,y)=(-1,0),不定方程x3-1=1 379y2仅有整数解(x,y)=(1,0);所使用的代数方法可以推广到求解大系数的三次不定方程中去. |
关键词: 不定方程 正整数解 递归数列 同余式 |
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On the Diophantine Equation x3±1=1 379 y2 |
CAO Rui,LUO Ming
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School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China
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Abstract: |
There is no general conclusion about the solution of x3±1=Dy2(D>0) type Diophantine equation.The solvability of x3±1=Dy2 for Diophantine equation when D=1379 is studied.By using congruence, recursive sequence, quadratic remainder and some properties of solutions of Pell equations,it is proved that the Diophantine equation x3+1=1379y2has only integer solutions (x,y)=(-1,0),and that the Diophantine equation x3-1=1379y2 has only integer solutions (x,y)=(1,0).The algebraic method used can be extended to solve cubic Diophantine equations with large coefficients. |
Key words: Diophantine equation positive integer solution recursive sequence congruence |
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