Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.3

An Arithmetic Progression on Quintic Curves


Alejandra Alvarado
Department of Mathematics
University of Arizona
617 N. Santa Rita Ave.
Tucson, AZ 85721
USA

Abstract:

Consider a degree five curve of the form $ y^2=f(x)$ where $ f(x)\in \mathbb{Q} [x]$. Ulas previously showed the existence of an infinite family of curves $ C$ which contain an arithmetic progression (AP) of length 11. The author also found an example of said curve which contains 12 points in AP. In this paper, we construct an infinite family of curves with an AP of length 12.
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Received August 16 2009; revised version received October 19 2009. Published in Journal of Integer Sequences, October 21 2009.

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