关于幂和丢番图方程S_5(x)=y^n

On the Sum of Equal Powers and Diophantine Equation S_5(x) =y^n

获得了幂和丢番图方程S_5(x)=yn有正整数解的充要条件：得到了当n=2时该方程有无穷多组正整数解的解集公式；证明了当n＝3和n≥4为偶数时，该方程仅有解（x,y）=（1．1）．

The necessary and sufficient condition that the sum of equal powers and Diophantine equaion S5(x) =yn have positive integer solutions are presented. The equation has general purpose formula for n=2 and the eguation an only solution (x, y) = (1, 1) for n = 3 and n≥4 (n is even number)