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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 $n=14$.

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