| 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 |
| DOI： |
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| On the Diophantine Equation x3+1=158y2 |
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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 |
