Naslov
On some applications of a theorem of Worley

Autori
Jadrijević, Borka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo

Izvornik
27th Journees Arithmetiques / - Vilnius : Vilnius University, 2011, 54-54

Skup
27th Journees Arithmetiques

Mjesto i datum
Vilnius, Litva, 27.06.2011. - 01.07.2011

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
diophantine approximations; continued fractions; Thue equations

Sažetak
The following result of Worley and Dujella extends classical results of Legendere and Fatou concerning Diophantine approximations of the form |alpha - a/b| < 1/2b^2
and |alpha - a/b| < 1/b^2: Let alpha be a real number and a and b coprime nonzero integers, satisfying the inequality |alpha - a/b| < M/b^2 ; where M is a positive real number. Then (a, b) = (rp_{;n+1}; +- up_n, rq_{;n+1}; +- uq_n), for some n  >= -1 and nonnegative integers r and u such that ru < 2M ; where p_n=q_n denotes the n-th convergent of alpha. This result is very useful for solving various types of problems that can be reduced to solving a parametric Pellian equation or a system of the parametric Pellian equations with bounded right hand side. In this talk we will present a few results obtained in this way.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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