丢番图方程x(x+1)=Dy^2和x(kx+1)~n=p1p2…p_my^n

Diophantine equation x(x+1)=Dy^2 and x(kx+1)~n=p1p2…p_my^n

多项式整数值中的完全方幂问题,是数论中引入关注的研究课题,本文利用pell方程解的性质,给出了丢番图方程x(x+1)=Dy^2和x(kx+1)~n=p1p2…p_my^n的所有正整数解.

This article uses the nature of pell＇s equation, and gives all the positive interber solutions to the Diophantine equation x（x＋1）=Dy^2 and x（kx＋1）^n=p1p2…pmy^n