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On arithmetic progressions on Pellian equations (CROSBI ID 133133)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej ; Petho, Attila ; Tadić, Petra On arithmetic progressions on Pellian equations // Acta mathematica Hungarica, 120 (2008), 1-2; 29-38. doi: 10.1007/s10474-007-7087-1

Podaci o odgovornosti

Dujella, Andrej ; Petho, Attila ; Tadić, Petra

engleski

On arithmetic progressions on Pellian equations

We consider arithmetic progressions consisting of integers which are y-components of solutions of an equation of the form x^2-dy^2=m. We show that for almost all four-term arithmetic progressions such an equation exists. We construct a seven-term arithmetic progression with the given property, and also several five-term arithmetic progressions which satisfy two different equations of the given form. These results are obtained by studying the properties of a parametric family of elliptic curves.

Pell equation; arithmetic progression; elliptic curves

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Podaci o izdanju

120 (1-2)

2008.

29-38

objavljeno

0236-5294

10.1007/s10474-007-7087-1

Povezanost rada

Matematika

Poveznice
Indeksiranost