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Arithmetic Progressions on Conics

Published

Author(s)

Abdoul Aziz Ciss, Dustin Moody

Abstract

In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We also provide infinite families of three term progressions on the unit hyperbola, as well as conics ax^2+cy^2=1 containing arithmetic progressions as long as 8 terms.
Citation
Journal of Integer Sequences
Volume
20

Keywords

arithmetic progression, conic

Citation

Aziz Ciss, A. and Moody, D. (2016), Arithmetic Progressions on Conics, Journal of Integer Sequences, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=922948 (Accessed July 20, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created December 26, 2016, Updated October 12, 2021