14-term arithmetic progressions on quartic elliptic curves
Journal of integer sequences, Tome 9 (2006) no. 1
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 $n=14$.
@article{JIS_2006__9_1_a6,
author = {MacLeod, Allan J.},
title = {14-term arithmetic progressions on quartic elliptic curves},
journal = {Journal of integer sequences},
year = {2006},
volume = {9},
number = {1},
zbl = {1101.11018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_1_a6/}
}
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/