| 关于方程x~2+D~m=p~n和方程x~2+2~m=y~n |
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| 引用本文： | 孙琦
,曹珍富.关于方程x~2+D~m=p~n和方程x~2+2~m=y~n[J].四川大学学报(自然科学版),1988(2). |
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| 作者姓名： | 孙琦 曹珍富 |
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| 作者单位： | 哈尔滨工业大学 |
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| 基金项目： | 国家自然科学基金,青年奖励研究基金资助项目 |
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| 摘 要： | 设D为正整数、P为不能整除D的奇素数.本文研究关于正整数x,m,n的Diophantine方程x~2+D~m=p~n.主要结果是定理1—3,并且给出了方程x~2+2~m=y~n(n>2,2|y)的所有正整数解。
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| 关 键 词： | Diophantine方程 正整数解 素数 理想 |
ON TH DIOPHANTINE EQUATIONS x~2+ D~m = P~n AND x~2+2~m=y~n |
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| Sun Qi Cao Zhenfu.ON TH DIOPHANTINE EQUATIONS x~2+ D~m = P~n AND x~2+2~m=y~n[J].Journal of Sichuan University (Natural Science Edition),1988(2). |
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| Authors: | Sun Qi Cao Zhenfu |
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| Institution: | Sun Qi Cao Zhenfu |
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| Abstract: | Let D be a positive integer and p a prime number not dividing D. In this paper we consider the Diophantine equationin positivs x,m,nt Main results are given in Theorem 1-3.These results contained the greater part of M. Yamabe, M. Kutsuna and M. Toyoizumi's ones, and our proofs are more elementary and more clear.In addition,we gave all positive integer solutions of the Diophantine equation xi + 2m = y" (n>2)when 2\y as follow.(m, n, x, y) = (6s+1, 3, 23s.5, 22S-3),(6s + 2, 3,23s. 11,22S . 5), (4s+5, 4, 22s . 7,2s - 3),(10t+ 5, 5, 25t-3. 11, 22t-1 . 3) and (2st + s + t) , 2s+ 1. |
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| Keywords: | Diophantine equation positive integer solution prime number ideal |
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