# Mathematical Communications,Vol. 17 No. 2, 2012

Original scientific paper

Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$

Khalil Ayadi ; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie
Mohamed Hbaib ; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie
Faiza Mahjoub ; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie

 Fulltext: english, pdf (280 KB) pages 613-627 downloads: 570* cite APA 6th EditionAyadi, K., Hbaib, M. & Mahjoub, F. (2012). Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$. Mathematical Communications, 17 (2), 613-627. Retrieved from https://hrcak.srce.hr/93295 MLA 8th EditionAyadi, Khalil, et al. "Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$." Mathematical Communications, vol. 17, no. 2, 2012, pp. 613-627. https://hrcak.srce.hr/93295. Accessed 1 Aug. 2021. Chicago 17th EditionAyadi, Khalil, Mohamed Hbaib and Faiza Mahjoub. "Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$." Mathematical Communications 17, no. 2 (2012): 613-627. https://hrcak.srce.hr/93295 HarvardAyadi, K., Hbaib, M., and Mahjoub, F. (2012). 'Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$', Mathematical Communications, 17(2), pp. 613-627. Available at: https://hrcak.srce.hr/93295 (Accessed 01 August 2021) VancouverAyadi K, Hbaib M, Mahjoub F. Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$. Mathematical Communications [Internet]. 2012 [cited 2021 August 01];17(2):613-627. Available from: https://hrcak.srce.hr/93295 IEEEK. Ayadi, M. Hbaib and F. Mahjoub, "Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$", Mathematical Communications, vol.17, no. 2, pp. 613-627, 2012. [Online]. Available: https://hrcak.srce.hr/93295. [Accessed: 01 August 2021]

Abstracts
In this paper, with different approaches we study rational
approximation for the algebraic {formal power series} in
$\mathbb{F}_{2}((X^{-1}))$ solving the irreducible equation
$\alpha^{3}=R,$
where $R$ is a polynomial of $\mathbb{F}_{2}[X]$.
Moreover, for some polynomials $R$, we give explicitly the
continued fraction expansion of the root of this equation.

Hrčak ID: 93295

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