In this article， the sum of two squares and Gauss theorem is used to solve a particular diophantus equation 〖SX(〗1〖〗x2〖SX)〗+〖SX(〗1〖〗y2〖SX)〗=〖SX(〗1〖〗z2〖SX)〗+〖SX(〗1〖〗w2〖SX)〗. 〖SX(〗1〖〗x2〖SX)〗+〖SX(〗1〖〗y2〖SX)〗=〖SX(〗1〖〗z2〖SX)〗+〖SX(〗1〖〗w2〖SX)〗 will be converted to a2+b2=c2+d2. After discussion,a2+b2≡c2+d2≡1,2(mod 4). We say that a2+b2≡c2+d2≡1(mod 4) if and only if (k1-k3)(k1+k3-1)≡(k4+k2)(k4-k2)≡0(mod 4); we say that a2+b2≡c2+d2≡2(mod 4) if and only if (k1-k3)(k1+k3-1)≡(k4-k2)(k4+k2-1)≡0,2(mod 4).