丢番图方程sum from k=0 to n k^4=ny^2,sum from k=0 to n k^3=np_2p_2…p_my^2以及sum from k=0 to n k^5=ny^2

Diophantine equation sum from k=0 to n k^4=ny^2,sum from k=0 to n k^3=np_2p_2…p_my^2 and sum from k=0 to n k^5=ny^2

多项式整数值中的完全方幂问题,是数论中引人关注的研究课题.本文利用pell方程解的性质,给出了丢番图方程sum from k=0 to n k^4=ny^2,sum from k=0 to n k^3=np_2p_2…p_my^2以及sum from k=0 to n k^5=ny^2的所有正整数解。

This article uses the nature ofpell＇s equation, and gives all the positive interber solutions to the Diophantine equation ∑k=1 n k4=ny2 ∑k=1 n k3=np1p2…pmy2以及∑k=1 n k5=ny2.