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A Note on Arithmetic Progressions on Quartic Elliptic Curves
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Maciej Ulas

Jagiellonian University

Institute of Mathematics

Reymonta 4

30-059 Kraków

Poland

**Abstract:**
G. Campbell
described a technique for
producing infinite families of quartic elliptic curves containing
a length-9 arithmetic progression. He also gave an example of a
quartic elliptic curve containing a length-12 arithmetic
progression. In this note we give a construction of an infinite
family of quartics on which there is an arithmetic progression of
length 10. Then we show that there exists an infinite family of
quartics containing a sequence of length 12.

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Received November 11 2004;
revised version received May 21 2005.
Published in *Journal of Integer Sequences* May 24 2005.

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