Geodesic
14-term arithmetic progressions on quartic elliptic curves
Journal of integer sequences, Tome 9 (2006) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $P_4(x)$ be a rational quartic polynomial which is not the square of a quadratic. Both Campbell and Ulas considered the problem of finding an rational arithmetic progression $x_1,x_2,\ldots,x_n$, with $P_4(x_i)$ a rational square for $1 \le i \le n$. They found examples with $n=10$ and $n=12$. By simplifying Ulas' approach, we can derive more general parametric solutions for $n=10$, which give a large number of examples with $n=12$ and a few with $n=14$.
Classification : 11G05, 11B25
Keywords: arithmetic progression, quartic, elliptic curve 
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     author = {MacLeod, Allan J.},
     title = {14-term arithmetic progressions on quartic elliptic curves},
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MacLeod, Allan J. 14-term arithmetic progressions on quartic elliptic curves. Journal of integer sequences, Tome 9 (2006) no. 1. http://geodesic.mathdoc.fr/item/JIS_2006__9_1_a6/