engleski

A method of constructing Diophantine quadruples in some number fields

Let R be a commutative ring with unity 1 and w 2 R. We say that a set of four nonzero distinct elements in R is a Diophantine quadruple with the property D(w) if the product of any two distinct elements increased by w is a perfect square. Such sets can be constructed e ectively using polynomial formulas. The aim of this is to verify the conjecture that the existence of a Diophantine quadruple with the property D(w) depends on the representability of w as a difference of two squares of elements in some number fields.

Diophantine quadruples; number fields

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