Abstract
Let n ⩾ 5 be an integer. We provide an effective method for finding all elliptic curves in short Weierstrass form E / Q with j ( E ) ∈ { 0 , 1728 } and all P ∈ E ( Q ) such that the nth term in the elliptic divisibility sequence defined by P over E fails to have a primitive divisor. In particular, we improve recent results of Everest, Mclaren, and Ward on the Zsigmondy bounds of elliptic divisibility sequences associated with congruent number curves.
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