This paper studies the problem of left divisibility in a semigroup given by a single defining relation of the form $a=bA$ , where $A$ is an arbitrary word in the alphabet $a,b$ . Solvability of the problems of equality and left divisibility of words is proved for a semigroup given by a defining relation of the form $a=(bA)^na$ , where $n>1$ . Bibliography: 4 titles.