摘要
设d是1个给定的正整数且不是平方数,利用Pell方程的解法和高次Diophantine方程的结果研究了4个指数Diophantine方程:(i)2 21nx-dp=,(ii)2 21np-dx=,(iii)2 21nx-dp=-,(iv)2np-2dx=-1的解(x,p,n),其中p是素数,x,n是正整数,完整地解决了方程(i)和当n≥2时方程(ii)、当2d≠t+1时方程(iii)、当d>2时方程(iv)的求解问题.
Let d be a given positive integer and not a square number, using the solutions of Pell equation and the results of high power Diophantine equation, the following four exponential Diophantine equations are studied：（i）2 21nx-dp =,（ii） 2 21np-dx =,（iii）2 21nx-dp =-,（iv）2 21np-dx =-, where p are some prime numbers, both x and n are some positive integers. The complete solutions are obtained for the equation（i） and equation（ii） when n ≥2, equation（iii） when 2d ≠t＋1, equation（iv） when d 2.
出处
《宁波大学学报（理工版）》
CAS
2015年第2期60-62,共3页
Journal of Ningbo University：Natural Science and Engineering Edition
