Diophantine problems involving recurrence sequences have a long history and
is an actively studied topic within number theory. In this paper, we connect to
the field by considering the equation \begin{align*} B_mB_{m+d}\dots
B_{m+(k-1)d}=y^\ell \end{align*} in positive integers m,d,k,y with
gcd(m,d)=1 and k≥2, where ℓ≥2 is a fixed integer and
B=(Bn)n=1∞ is an elliptic divisibility sequence, an important class
of non-linear recurrences. We prove that the above equation admits only
finitely many solutions. In fact, we present an algorithm to find all possible
solutions, provided that the set of ℓ-th powers in B is given. (Note
that this set is known to be finite.) We illustrate our method by an example.Comment: To appear in Bulletin of Australian Math Societ