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https://doi.org/10.3336/gm.47.1.04

A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1

Maohua Le ; Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong 524048, P.R. China

Puni tekst: engleski, pdf (102 KB) str. 53-59 preuzimanja: 275* citiraj
APA 6th Edition
Le, M. (2012). A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1. Glasnik matematički, 47 (1), 53-59. https://doi.org/10.3336/gm.47.1.04
MLA 8th Edition
Le, Maohua. "A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1." Glasnik matematički, vol. 47, br. 1, 2012, str. 53-59. https://doi.org/10.3336/gm.47.1.04. Citirano 28.10.2021.
Chicago 17th Edition
Le, Maohua. "A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1." Glasnik matematički 47, br. 1 (2012): 53-59. https://doi.org/10.3336/gm.47.1.04
Harvard
Le, M. (2012). 'A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1', Glasnik matematički, 47(1), str. 53-59. https://doi.org/10.3336/gm.47.1.04
Vancouver
Le M. A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1. Glasnik matematički [Internet]. 2012 [pristupljeno 28.10.2021.];47(1):53-59. https://doi.org/10.3336/gm.47.1.04
IEEE
M. Le, "A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1", Glasnik matematički, vol.47, br. 1, str. 53-59, 2012. [Online]. https://doi.org/10.3336/gm.47.1.04

Sažetak
Let m,n be positive integers with 1 < m < n. Let δ be a positive number with 1/2 < δ < 1 . In this paper we prove that if gcd(m,n)>nδ and n>(8× 1016(log(1016/θ3))3/θ3)1/θ, where θ=min(1-δ, 2δ-1), then the simultaneous Pell equations x2-(m2-1)y2=1 and z2-(n2-1)y2=1 have only one positive integer solution (x,y,z)=(m,1,n).

Ključne riječi
Simultaneous Pell equations; number of solutions

Hrčak ID: 82570

URI
https://hrcak.srce.hr/82570

Posjeta: 501 *