引用本文: | 李小丽, 罗明.关于不定方程 x3+1=158y2(J/M/D/N,J:杂志,M:书,D:论文,N:报纸).期刊名称,2019,36(5):77-81 |
| 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 x3+1=158y2 |
李小丽, 罗明1
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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: |
关于不定方程 x3±1=Dy2(D>0)所有整数解的求解问题,当D有6k+1形的素因数时,方程的解比较困难;当D=158时,不定方程 x3±1=Dy2,主要运用Pell方程、递归数列等方法证明了仅有整数解(-1,0),(293,±399). |
关键词: 不定方程 整数解 递归数列 平方剩余 |
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On the Diophantine Equation x3+1=158y2 |
LI Xiao-li, LUO Ming
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Abstract: |
On the Indefinite Equation,there have been a lot of researches, when the D doesn‘t has the prime factor shape of 6k+1,all of its solutions have been obtained by Ke Zhao, Sun Qi, Cao Zhenfu, Liu Peijie, and so on.When the prime factor has the shape of 6k+1, the solution of the equation is difficult.Current equation x3+1=158y2(D>0),when D<100,all cases have been resolved (see Table 3).But when 200>D>100,it's not finished yet.By using the Pell Equation, the method of Recursive Sequence proved that when D=158,the Diophantine equation x3+1=158y2 has only integer solution(x,y)=(-1,0),(293,±399). |
Key words: Diophantine equation integer solution recursive sequence quadratic residue |
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