Positive values of inhomogeneous quinary quadratic forms of type (4,1)

Abstract Here it is proved that if Q(x, y, z, t, u) is a real indefinite quinary quadratic form of type (4,1) and determinant D , then given any real numbers x 0 , y 0 , z 0 , t 0 , u 0 there exist integers x, y, z, t, u such that All critical forms are also obtained.