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We prove that there are finitely many perfect powers in elliptic divisibilitysequences generated by a non-integral point on elliptic curves of the from$y^2=x(x^2+b)$, where $b$ is any positive integer. We achieve this by using themodularity of elliptic curves over real quadratic number fields.

On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences