如果a, b是互素奇数,雅可比符号(a/-b)定义成和(a/b)相等的话
当a≡1(mod 4)时,(b/a)=(-b/a),(a/-b)=(a/b),所以(a/-b)*(-b/a)= (a/b)*(b/a)
右边 (-1)^[(a-1)/2*(-b-1)/2] = 1 = (-1)^[(a-1)/2*(b-1)/2]
当a≡3(mod 4)时,(b/a)= -(-b/a),(a/-b)=(a/b),所以(-b/a)*(a/-b) = -(b/a)*(a/b)
右边 (-1)^[(a-1)/2*(-b-1)/2] = (-1)^[(-b-1)/2] = -(-1)^[(b-1)/2] = -(-1)^[(a-1)/2*(b-1)/2]
所以只要这个式子对(a, b), (a, -b), (-a, b), (-a, -b)中的某一对成立,那对这4对全都成立
当a≡1(mod 4)时,(b/a)=(-b/a),(a/-b)=(a/b),所以(a/-b)*(-b/a)= (a/b)*(b/a)
右边 (-1)^[(a-1)/2*(-b-1)/2] = 1 = (-1)^[(a-1)/2*(b-1)/2]
当a≡3(mod 4)时,(b/a)= -(-b/a),(a/-b)=(a/b),所以(-b/a)*(a/-b) = -(b/a)*(a/b)
右边 (-1)^[(a-1)/2*(-b-1)/2] = (-1)^[(-b-1)/2] = -(-1)^[(b-1)/2] = -(-1)^[(a-1)/2*(b-1)/2]
所以只要这个式子对(a, b), (a, -b), (-a, b), (-a, -b)中的某一对成立,那对这4对全都成立