  We prove that the $p$th Hecke operator on the Morava $E$-cohomology of a
space is congruent to the Frobenius mod $p$. This is a generalization of the
fact that the $p$th Adams operation on the complex $K$-theory of a space is
congruent to the Frobenius mod $p$. The proof implies that the $p$th Hecke
operator may be used to test Rezk's congruence criterion.
