| 关于勾股丢番图方程x~2+(x+k)~2=z~2 |
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| 引用本文： | 何金敏,王庆平.关于勾股丢番图方程x~2+(x+k)~2=z~2[J].齐齐哈尔大学学报(自然科学版),1997(2). |
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| 作者姓名： | 何金敏 王庆平 |
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| 作者单位： | 齐齐哈尔铁路运输职工大学 |
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| 摘 要： | 本文给出了勾股丢番图方程x2＋（x＋k）＝z2有正整数解的充要条件以及使该方程有正整数解k的必要条件，并根据k＝1，7时的正整数解，给出了对于给定k求该方程正整数解的一般方法。
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| 关 键 词： | 丢番图方程 Pell方程 基本解 |
On the Pythagorean Diophantine Equation x~2+(x+k)~2=z~2 |
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| He Jinmin ,Wang Qingping.On the Pythagorean Diophantine Equation x~2+(x+k)~2=z~2[J].Journal of Qiqihar University(Natural Science Edition),1997(2). |
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| Authors: | He Jinmin Wang Qingping |
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| Institution: | Qiqihar Railway Worker-staff University |
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| Abstract: | In this paper the general recurrence forrmula of solution of pythagorean diophantine equation x2+(x+k)2=z2 is given f which contains the necessary and sufficent condition of squad whole number solution. and the squad whole number suiution k. According to the whole number solution when k=1.7. the general method of solving one saiad whole number of the equation by giving regular k is given. |
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| Keywords: | Diophantine equation Pell's equation Basic solution |
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