Brahmagupta Triangles in Generalized Fibonacci Sequences
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Abstract
For any positive integers and
, define the sequence
by
,
, and
for all
. A Brahmagupta triangle is a triangle all of whose side lengths are consecutive positive integers with integral area. In this paper, we prove that for any given
and
, there is at most one Brahmagupta triangle all of whose side lengths are elements of
. Moreover, we characterize all initial values
for which the sequence
contains a Brahmagupta triangle, and show that this occurs precisely in two Pell-parametrized families.
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