Journal of Integer Sequences, Vol. 19 (2016), Article 16.6.3 |

Department of Mathematics

Faculty of Science

Cairo University

Giza

Egypt

Mohammad Sadek

Mathematics and Actuarial Science Department

American University in Cairo

AUC Avenue

New Cairo

Egypt

**Abstract:**

Let *C* be a hyperelliptic curve over
described by
,
.
The points
,
,
are said to be in a geometric progression of length *k* if the rational numbers *x*_{i},
,
form a geometric progression sequence in
,
i.e.,
*x*_{i} = *pt*^{i} for some
.
In this paper we prove the existence of an infinite family of hyperelliptic curves on which there is a sequence of rational points in a geometric progression of length at least eight.

Received February 18 2016; revised versions received June 14 2016; June 17 2016.
Published in *Journal of Integer Sequences*, June 29 2016.

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