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Arithmetic Progressions on Huff Curves
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Ajai Choudhry

13/4 A Clay Square

Lucknow - 226001

India

**Abstract:**

Several mathematicians have studied the problem of finding a set of n
rational points on various models of elliptic curves such that the
abscissae of these n points are in arithmetic progression. This paper
is concerned with finding such arithmetic progressions on the Huff
model of elliptic curves. Moody has found arithmetic progressions of
length 9 on several infinite families of Huff curves with numerical
coefficients. In this paper we find infinitely many parametrized
families of Huff curves on which there are arithmetic progressions of
length 9, as well as several Huff curves on which there are arithmetic
progressions of length 11.

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Received January 1 2015; revised version received March 23 2015.
Published in *Journal of Integer Sequences*, May 19 2015.

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