摘要
本文用初等方法给出了当2■m时方程1+q+q^2+…+q^(-1)=p^m,p,q是奇素数,n≥5,m≥2有解的充要条件,并且证明了当q(q-1)p<100或p=q(q-1)t^2±1时该方程只有一个已知解。
In this paper, the elementary proofs of the following theorems are given(1)If 2m, then the equation 1+q+q^2+…+q^(n-1)=p^m, (p·q are odd primes, n≥5,m≥2)(*) has solution if and only if fundamental solution to the Pell equation x^2-q (q-1)py^2=1 is ε=q^n+(q-1)p^m+2q n-1/2 p m-1/2 (q(q-1)P)^(1/2).(2)If 2m, q(q-1)p<100 or p=q(q-1)t^2+1, where t is positive integer, then the equation (*) has no solution.
出处
《哈尔滨工业大学学报》
EI
CAS
CSCD
北大核心
1992年第3期6-9,共4页
Journal of Harbin Institute of Technology
关键词
丢番图方程
解
Diophantine equation
solution
