| 关于丢番图方程|3x-2y|=p |
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| 引用本文： | 周科. 关于丢番图方程|3x-2y|=p[J]. 广西师范学院学报(自然科学版), 2007, 24(4): 36-39 |
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| 作者姓名： | 周科 |
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| 作者单位： | 广西师范学院,数学与计算机科学系,广西,南宁,530001 |
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| 摘 要： | 设p为素数,x,y正整数.在文献中,周科证明了p=41,43,53,59,67,71,83,87,97时,方程|3x-2y|=p没有解;证明了方程在p=5,7,13,23时有超过一组的解并给出了所有解,该文证明了当p=31,37,47,61,73,79时,该方程有唯一解,并给出了相应解.
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| 关 键 词： | 素数 丢番图方程 整数解 |
| 文章编号： | 1002-8743（2007）04-0036-04 |
| 收稿时间： | 2007-07-21 |
| 修稿时间： | 2007-07-21 |
Unique Solution to The Diophantine Equation |3x - 2y| = p |
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| ZHOU Ke. Unique Solution to The Diophantine Equation |3x - 2y| = p[J]. Journal of Guangxi Teachers Education University:Natural Science Edition, 2007, 24(4): 36-39 |
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| Authors: | ZHOU Ke |
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| Abstract: | Let p be prime number,x and y be positive integral numbers,the propositions that when p=41,43,53,59,67,71,83,87,97,the Diophantine equation |3x-2y|=p has no integral solution,and the equation has more than a group of solution when p=5,7,13,23 that has been proved by Zhou Ke.In this paper,we study the unique solution to this equation in case p=31,37,47,61,73,79,also all of those integral solutions will be given. |
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| Keywords: | prime Diophantine equation positive integral solution |
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