Geometric progression of length four on the circle
*Irshad AyoobCorresponding authoriayoub@psu.edu.saDepartment of Mathematics and General Sciences Prince Sultan University P. O. Box 66833Riyadh, 11586, Saudi Arabia0000-0002-1936-9540View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Oct 2024
- Published Online:
- 18 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2240
- Pages:
- 2025–2030
Abstract
Keywords
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References
[1] G. Campbell, “A note on arithmetic progressions on elliptic curves,” J. Integer Sequences, vol. 6, Article 03.1.3 (2003).
[2] A. Bremner, “On arithmetic progressions on elliptic curves,” Experiment. Math., vol. 8, pp. 409–413 (1999).
[3] A. MacLeod, “14-term arithmetic progressions on quartic elliptic curves,” J. Integer Sequences, vol. 9, Paper 06.1.2 (2006).
[4] I. García-Selfa and J. M. Tornero, “Searching for simultaneous arithmetic progressions on elliptic curves,” Bull. Austral. Math. Soc., vol. 71, pp. 417–424 (2005).
[5] M. Ulas, “A note on arithmetic progressions on quartic elliptic curves,” J. Integer Sequences, vol. 8, Paper 05.3.1 (2005).
[6] J. B. Lee and W. Y. Vélez, “Integral solutions in arithmetic progression for y2 = x3 + k, Period. Math. Hung., vol. 25, pp. 31–49, 1992.
[7] D. Moody, “Arithmetic progressions on Edwards curves,” J. Integer Sequences, vol. 14, Article 11.1.7 (2011).
[8] D. Moody, “Arithmetic progressions on Huff curves,” Ann. Math. Inform., vol. 38, pp. 111–116 (2011).
[9] A. Bremner, “Arithmetic progressions on Edwards curves,” J. Integer Sequences, vol. 16, Article 13.8.5 (2013).
[10] A. Choudhry, “Arithmetic progressions on Huff curves,” J. Integer Sequences, vol. 18, Article 15.5.2 (2015).
[11] E. González-Jiménez, “On arithmetic progressions on Edwards curves,” Acta Arith., vol. 167, pp. 117–132 (2015).
[12] A. A. Ciss and D. Moody, “Geometric progressions on elliptic curves,” Glas. Mat., vol. 52, pp. 1–10 (2017).
[13] M. Kamel and M. Sadek, “On sequences of consecutive squares on elliptic curves,” Glas. Mat., vol. 52, pp. 45–52 (2017).
[14] G. S. Çelik and G. Soydan, “Elliptic curves containing sequences of consecutive cubes,” Rocky Mountain J. Math., vol. 48, pp. 2163–2174 (2018).
[15] A. Choudhry and A. Juyal, “Rational points in arithmetic progression on the unit circle,” J. Integer Sequences, vol. 19, Article 16.4.1 (2016).
[16] A. A. Ciss and D. Moody, “Arithmetic progressions on conics,” J. Integer Sequences, vol. 20, Article 17.2.6 (2017).
[17] G. S. Çelik, M. Sadek, and G. Soydan, “Rational points in geometric progression on the unit circle,” Publ. Math. Debrecen, vol. 98, no. 3–4, pp. 513–520 (2021).
[18] M. S. A. Shukor and M. Y. A. Shukor, “A treaty of symmetric function: An approach in deriving general formulation for sums of power for an arbitrary arithmetic progression. Part 1,” J. Discrete Math. Sci. Cryptogr., vol. 23, no. 3, pp. 661–728 (2020). DOI: 10.1080/09720529.2015.1102945.
