摘要
讨论了丢番图方程3n+px2=yp(x,y,n∈N;p是奇素数)的可解性,得到以下结果:(1)当p=3时,方程的所有解为(x,y,n)=(46.33t+1,13.32t+1,6t+7),(10.33t+1,7.32t+1,6t+8).(2)当p≡1(mod 24)时,方程没有解.
The solvability of Diophanine equation 3n＋px2=y^p was investigated in this paper. If p =3, the equation has only solution （x,y,n）=（46·3^3t＋1,13·3^2t＋1,6t＋7）,（10·3^3t＋1,7·3^2t＋1,6t＋8）.If p =1 （mod 24）, then the equation has no solution.
出处
《河南科学》
2011年第12期1416-1420,共5页
Henan Science
基金
Research Project of Henan University of Technology(2006XJC038)
关键词
丢番图方程
二次数域
类数
Diophanine equation
quadratic number field
class number
