On real solutions of systems of equations

Systems of equations f1 = = fn−1 = 0 in ℝn = {x} having the solution x = 0 are considered under the assumption that the quasi-homogeneous truncations of the smooth functions f1,.., fn−1 are independent at x ≠ 0. It is shown that, for n ≠ 2 and n ≠ 4, such a system has a smooth solution which passes through x = 0 and has nonzero Maclaurin series. © 2017, Springer Science+Business Media, LLC, part of Springer Nature.