| 不定方程X2＋k2=y3的有理整解 |
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| 引用本文： | 拓小泉,郭金保,彭娟.不定方程X2＋k2=y3的有理整解[J].延安大学学报(自然科学版),2013,32(1):4-5. |
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| 作者姓名： | 拓小泉 郭金保 彭娟 |
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| 作者单位： | 延安大学数学与计算机科学学院,陕西延安,716000 |
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| 摘 要： | 利用了数论初等方法，讨论了k是有理素数p≡1mod4）且k=e2＋1,e∈Z为偶数和k是有理素数P≡3（mod4）的相伴数和，方程x2＋k2=y3的解的情况。
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| 关 键 词： | 不定方程 有理整数解 Gauss数环 整除 不可约数 |
On the Rational Integer Solutions of Diophantine Equations x2 +k2 =y3 |
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| TUO Xiao-quan
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GUO Jin-bao
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PENG JUAN.On the Rational Integer Solutions of Diophantine Equations x2 +k2 =y3[J].Journal of Yan'an University(Natural Science Edition),2013,32(1):4-5. |
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| Authors: | TUO Xiao-quan GUO Jin-bao PENG JUAN |
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| Institution: | (College of Mathematics and Computer Science,Yan an University,Yan an 716000,China) |
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| Abstract: | Using the methods of elementary number theory, It discussed the k is rational prime p ≡ 1 （ rood 4 ） and k=e2＋1,e∈Z, for even and k is rational prime number p ≡3 （ rood 4） companions number, the solution of the e- quation x2 ＋ k2 = y3. |
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| Keywords: | diophantine equation rational integer solutions Gauss number rings divisible irreducible number |
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