The Problem of Diophantus and Davenport for Gaussian Integers
نویسندگان
چکیده
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 Gaussian 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 6∈ {±2,±1 ± 2i,±4i}, then there exists at least one quadruple with the property D(z). Mathematics Subject Classification (1991): 11D09.
منابع مشابه
The problem of Diophantus and Davenport ∗
In this paper we describe the author’s results concerning the problem of the existence of a set of four or five positive integers with the property that the product of its any two distinct elements increased by a fixed integer n is a perfect square.
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