Naslov
The problem of Diophantus in some quadratic fields

Autori
Franušić, Zrinka

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

Izvornik
25th Journees Arithmetiques / Cremona, John ; Greaves, George ; Smyth, Chris - Edinburgh : University of Edinburgh, 2007, 14-15

Skup
25th Journees Arithmetiques

Mjesto i datum
Edinburgh, Ujedinjeno Kraljevstvo, 02.07.2007. - 06.07.2007

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Quadratic fields; Diophantine quadruples

Sažetak
Under the assumption of solvability of certain Pellian equations, we solve the problem of Diophantus for integers in some quadratic fields. This problem deals with the existence of four-element sets of integers such that the product of each two distinct elements increased by a fixed integer n is a perfect square. We effectively construct these sets using some polynomial formulas. Finally, we show that the problem is closely connected with the problem of representability of n as a difference of two squares.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA