Published: December 27, 2016
Citation: Journal of Integer Sequences vol. 20, no. 1, article no. 17.2.6 (December 27, 2016) pp. 1-8
Author(s)
Dustin Moody (NIST), Abdoul Aziz Ciss (École Polytechnique de Thiès)
Announcement
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 3- term progressions on the unit hyperbola, as well as conics ax^2 + cy^2 = 1 containing arithmetic progressions as long as 8 terms.
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...
See full 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 3- term progressions on the unit hyperbola, as well as conics ax^2 + cy^2 = 1 containing arithmetic progressions as long as 8 terms.
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Keywords
arithmetic progressions; conics
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