关于Diophantine方程xp-2p=pDy2

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On the Diophantine equation xp-2p=pDy2

摘要: 设p是奇素数,D是无平方因子正整数.本文证明了:当p3时,如果D不能被p或2kp+1之形素数整除,则方程xp-2p=pDy2没有适合gcd(x,y)=1的正整数解(x,y).
- 高次Diophantine方程 /
- 正整数解 /
- 存在性
Abstract: Let p be an odd prime,and let D be a positive integer with square free.It is proved that if p3 and D is not divisible by p or primes of the form 2kp+1,then the equation x~p-2~p=pDy~2 has no positive integer solutions (x,y) with gcd (x,y)=1.
- higher Diophantine equation /
- positive integer solution /
- existence