On arithmetic progressions on Pellian equations (CROSBI ID 133133)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano