关于丢番图方程1~5+2~5+…+x^5=y^2的通解公式

About the Solution Formula of the Diophantine Equation 1~5+2~5+…+x^5=y^2

证明了丢番图方程15+25+…+x5=y2必有无穷多组正整数解(xn,yn)=(xn,xn(x2n+1)un),且满足:xn+2=10xn+1-xn+4,x1=1,x2=13un+2=10un+1-un,u1=1,u2=11,给出了部分由计算机程序得到的解.

The fact has been proved that the equation 1^5＋2^5＋…＋x^5=y^2 has infinite groups positive integer solution （xn,yn）=（xn,xn（xn＋1）/2 un） and the solution contents with {xn＋2=10xn＋1-xn＋4,x1=1,x2=13, un＋2=10un＋1-un,u1=1,u2=11. A part of solution solved by computer has been given.