| 奇素数的三项方幂和中的平方数 |
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| 引用本文： | 刘志伟,汤千文. 奇素数的三项方幂和中的平方数[J]. 数学的实践与认识, 2009, 39(10) |
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| 作者姓名： | 刘志伟 汤千文 |
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| 作者单位： | 贺州学院,数学系,广西,贺州,542800 |
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| 摘 要： | 研究了一类基本而又重要的指数Diophantine方程,利用广义Ramanujan-Nagell方程的性质证明了这类方程有非负整数解的充要条件,并得出这类方程的全部非负整数解.
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| 关 键 词： | 指数Diophantine方程 素数方幂和 平方数 |
The Squares in Sums of Theree Odd Prime Powers |
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| LIU Zhi-wei,TANG Qian-wen. The Squares in Sums of Theree Odd Prime Powers[J]. Mathematics in Practice and Theory, 2009, 39(10) |
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| Authors: | LIU Zhi-wei TANG Qian-wen |
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| Abstract: | Let p be an odd prime.ln this paper we prove that if p>C, where C is an effectively computable absolute constant, then the equation pa+pb+pc=z2 has nonnegative integer solutions (a,b,c,z) if and only if p+2 is a perfect square.Moreover, if the above mentioned condition holds, then all solutions of the equation are (a,b,c,z)=(2d,2d,2d+1,pd(p+2)～(1/2), where dis a nonnegative integer. |
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| Keywords: | Exponential diophantine equation sum of prime powers perfect square |
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