  In this paper we state a problem on rigidity of powers, which has a strong
topological background for the rigid Hirzebruch genera and Kosniowski's
conjecture of unitary circle actions. However, our statement of this problem is
elementary enough and does not require any knowledge of algebraic topology. We
shall give a solution of this problem for some particular cases. As a
consequence, we obtain that Kosniowski's conjecture holds in the case of
dimension less than 11 or equal to 14.
