|Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.2|
Let 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 , with a rational square for . They found examples with and . By simplifying Ulas' approach, we can derive more general parametric solutions for , which give a large number of examples with and a few with .
Received October 25 2005; revised version received November 18 2005. Published in Journal of Integer Sequences November 18 2005.