In this note we provide a partial answer to a problem proposed by M. Brehr. We prove that if α , β are automorphisms of a commutative prime ring of characteristic not equal to 2 satisfying the equation α + α − 1 = β + β − 1 , then either α = β or α = β − 1 . As a consequence α and β commute and in this situation the equation itself ensures the commutativity of α and β .