engleski

Effective solution of the D(-1)-quadruple conjecture

The D(-1)-quadruple conjecture states that there does not exist a set of four positive integers such that the product of any two distinct elements is one greater than a perfect square. It is proved that if {; ; ; a ; b ; c ; d}; ; ; is such a set, then max{; ; ; a ; b ; c ; d}; ; ; < 10^{; ; ; 10^23}; ; ; , hence a proof of the conjecture is given up to a completely determined, finite (but currently computationally infeasible large) set of possible exceptions to check.

diophantine m-tuples; Pell equation; diophantine approximation

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