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.
Let p be an odd prime. In this paper we prove that if P 〉 C, where C is an effectively computable absolute constant, then the equation p^a＋p^b＋p^c =z^2 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, p^d √P＋2）, where dis a nonnegative integer.
出处
《数学的实践与认识》
CSCD
北大核心
2009年第10期161-164,共4页
Mathematics in Practice and Theory
基金
国家自然科学基金(10271104)
