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https://doi.org/10.3336/gm.52.1.04

On sequences of consecutive squares on elliptic curves

Mohamed Kamel ; 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

Puni tekst: engleski, pdf (107 KB) str. 45-52 preuzimanja: 509* citiraj
APA 6th Edition
Kamel, M. i Sadek, M. (2017). On sequences of consecutive squares on elliptic curves. Glasnik matematički, 52 (1), 45-52. https://doi.org/10.3336/gm.52.1.04
MLA 8th Edition
Kamel, Mohamed i Mohammad Sadek. "On sequences of consecutive squares on elliptic curves." Glasnik matematički, vol. 52, br. 1, 2017, str. 45-52. https://doi.org/10.3336/gm.52.1.04. Citirano 27.09.2020.
Chicago 17th Edition
Kamel, Mohamed i Mohammad Sadek. "On sequences of consecutive squares on elliptic curves." Glasnik matematički 52, br. 1 (2017): 45-52. https://doi.org/10.3336/gm.52.1.04
Harvard
Kamel, M., i Sadek, M. (2017). 'On sequences of consecutive squares on elliptic curves', Glasnik matematički, 52(1), str. 45-52. https://doi.org/10.3336/gm.52.1.04
Vancouver
Kamel M, Sadek M. On sequences of consecutive squares on elliptic curves. Glasnik matematički [Internet]. 2017 [pristupljeno 27.09.2020.];52(1):45-52. https://doi.org/10.3336/gm.52.1.04
IEEE
M. Kamel i M. Sadek, "On sequences of consecutive squares on elliptic curves", Glasnik matematički, vol.52, br. 1, str. 45-52, 2017. [Online]. https://doi.org/10.3336/gm.52.1.04

Sažetak
Let C be an elliptic curve defined over Q by the equation y2=x3+Ax+B where A,BQ. A sequence of rational points (xi,yi) C(Q), i=1,2,…, is said to form a sequence of consecutive squares on C if the sequence of x-coordinates, xi,i=1,2,…, consists of consecutive squares. We produce an infinite family of elliptic curves C with a 5-term sequence of consecutive squares. Furthermore, this sequence consists of five independent rational points in C(Q). In particular, the rank r of C(Q) satisfies r≥ 5.

Ključne riječi
Elliptic curves; rational points, sequences of consecutive squares

Hrčak ID: 183122

URI
https://hrcak.srce.hr/183122

Posjeta: 613 *