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The problem of Diophantus in some quadratic fields (CROSBI ID 528734)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Franušić, Zrinka The problem of Diophantus in some quadratic fields // 25th Journees Arithmetiques / Cremona, John ; Greaves, George ; Smyth, Chris (ur.). Edinburgh: University of Edinburgh, 2007. str. 14-15

Podaci o odgovornosti

Franušić, Zrinka

engleski

The problem of Diophantus in some quadratic fields

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.

Quadratic fields; Diophantine quadruples

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Podaci o prilogu

14-15.

2007.

objavljeno

Podaci o matičnoj publikaciji

25th Journees Arithmetiques

Cremona, John ; Greaves, George ; Smyth, Chris

Edinburgh: University of Edinburgh

Podaci o skupu

25th Journees Arithmetiques

predavanje

02.07.2007-07.07.2007

Edinburgh, Ujedinjeno Kraljevstvo

Povezanost rada

Matematika