| 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 the field of rational numbers. The connection is via the
celebrated algorithm known as
the 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, for a given curve, we can find all of
them easily 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
complexity and hence can never reach 0, the group identity.
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