| Abstract:
In this talk we explore the connection between integral points and
points of finite order in the group E(Q) of an elliptic curve E
defined over rationals. The connection is via the celebrated
algorithm known as Lutz-Nagell Theorem. This theorem says that
torsion points are integral and that their y coordinates are bounded.
This proves that for any elliptic curve Q, the number of torsion
points is finite and we can then find all of them easily for a given
curve by the familiar chord-tangent process. The basic idea is that
if a point P is not integral, then the points obtained by the
doubling process (read: tangents), namely P, 2P , 4P, 8P, increase in
height and hence can never reach 0, the group identity.
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