Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.4

Arithmetic Progressions on y2 = x3 + k

Pallab Kanti Dey and Bibekananda Maji
Harish-Chandra Research Institute
Allahabad - 211019


Many authors have studied the problem of finding sequences of rational points on elliptic curves such that either the abscissae or the ordinates of these points are in arithmetic progression. In this paper we obtain upper bounds for the lengths of sequences of rational points on curves of the type y2 = x3 + k, kQ \ {0}, such that the ordinates of the points are in arithmetic progression, and also when both the abscissae and the ordinates of the points are separately the terms of two arithmetic progressions.

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Received September 19 2015; revised versions received September 24 2015; May 8 2016; September 3 2016. Published in Journal of Integer Sequences, September 4 2016.

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