Glasnik Matematicki, Vol. 32, No.1 (1997), 1-10.

THE PROBLEM OF DIOPHANTUS AND DAVENPORT FOR GAUSSIAN INTEGERS

Andrej Dujella

Department of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia
e-mail: duje@math.hr


Abstract.   A set of Gaussian integers is said to have the property D(z) if the product of its any two distinct elements increased by z is a square of a Gaussian integer. In this paper it is proved that if a Gaussain integer z is not representable as a difference of the squares of two Gaussian integers, then there does not exist a quadruple with the property D(z), but if z is representable as a difference of two squares and if z is not in {+-2, +-1 +-2i, +-4i }, then there exists at least one quadruple with the property D(z).

1991 Mathematics Subject Classification.   11D09.

Key words and phrases.   Diophantine quadruple, property of Diophantus, Gaussian integers, Pell equation.


Glasnik Matematicki Home Page

closePristupačnostrefresh

Ako želite spremiti trajne postavke, kliknite Spremi, ako ne - vaše će se postavke poništiti kad zatvorite preglednik.