Let r be an odd integer with r>1.In this paper the author gives a necessary condition for(X,Y,Z) being a positive integer solution of the equation X~2+Y~2=Z~r with Y being a power of an odd prime.

• 设r是大于1的奇数；给出了方程X2+Y2=Zr的正整数解(X；Y；Z)中Y为奇素数方幂的必要条件.