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Abstract: In this paper we consider some problems of existence of sets of four natural numbers with property D(n), for any integer n. We prove that, for all integers e, there exist infinitely many sets of four natural numbers with property D(e^2). Indeed, we show how a set {a, b} with property D(e^2) can be extended to a set {a, b, c, d} with the same property, if ab is not a perfect square. The general case is also considered: sets with property D(n), when n need not be a perfect square. The main...

Generalization of a problem of Diophantus