The aim of this paper is to prove the following result: ''Let A be an associative ring with a nonzero unity and \(\phi\) an automorphism of the ring A. The following assertions are equivalent for the ring \(R=A[[ X,\phi ]]:\) (1) the ring R is right distributive; (2) R is a right Bezout ring, and all the maximal right ideals of the ring A are ideals in A; (3) A is a strictly regular countably injective ring on the right and on the left, and \(\phi (e)=e\) for all idempotents e of the ring A.