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 October 2, 2025)
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Arithmetic Progressions on Conics
Published
Author(s)
Abdoul Aziz Ciss,
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
Pub Type
Journals
Download Paper
Keywords
arithmetic progression, conic
Citation
Issues
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Created December 26, 2016, Updated October 12, 2021