  In 2008, Langevin and Leander determined the dual function of three classes
of monomial bent functions with the help of Stickelberger's theorem: Dillon,
Gold and Kasami. In their paper, they proposed one very strong condition such
that their method works, and showed that both Gold exponent and Kasami exponent
satisfy this condition. In 2018, Pott {\em et al.} investigated the issue of
vectorial functions with maximal number of bent components. They found one
class of binomial functions which attains the upper bound. They also proposed
an open problem regarding monomial function with maximal number of bent
components.
  In this paper, we obtain an interesting result about the condition of
Langevin and Leander, and solve the open problem of Pott {\em et al.}.
Specifically, we show that: 1) for a monomial bent function over
$\mathbb{F}_{2^{2k}}$, if the exponent satisfies the first part of the
condition of Langevin and Leander, then it satisfies the entire condition; 2)
$x^{2^k+1}$ is the only monomial function over $\mathbb{F}_{2^{2k}}$ which has
maximal number of bent components. Besides, as a byproduct, we dig out a very
nice property about Kloosterman sums.
