The problem of Diophantus in some quadratic fields (CROSBI ID 528734)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
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