摘要
研究指数Diophantine方程组2x+py=qz与p+2=q的可解性问题。利用初等及代数的方法,彻底解决了指数Diophantine方程组2x+py=qz与p+2=q的求解问题,得到其唯一的正整数解并且给出了证明。即设p>3和q是满足p+2=q的孪生素数,方程2x+py=qz仅有正整数解(x,y,z)=(1,1,1)。
To study the solvability of the exponential Diophantine system 2x ＋py = qz and p ＋ 2 = q. By using the elementary and algebraic methods, the problem of the exponential Diophantine system 2x ＋ py = qz and p ＋ 2 = q is solved completely. The only solution of this system is given and proved. That is to say, let p 〉 3 and q be a pair of twin primes such that 2x ＋py = qz. The equation 2x ＋py = qz has only the positive integer solution （x ,y,z） = （1,1, 1）.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第4期524-526,共3页
Journal of Northwest University（Natural Science Edition）
基金
国家自然科学基金资助项目(11226038)
陕西省教育厅专项基金资助项目(11JK0472
11JK0474)
西安工程大学博士科研基金资助项目(BS1016)
