engleski

Extensions of a D(4)-triple

We call a set of positive integers {; ; a, b, c}; ; a D(4)-triple if a product of each two elements of a triple increased by 4 is a perfect square. It is conjectured that a triple can be extended to a quadruple uniquely with an element d > max{; ; a, b, c}; ; . In this talk, we present new results that support the conjecture, such as some new bounds on the elements of a triple for which we have proven that conjecture holds, and an upper bound on the number of possible extensions of a D(4)- triple to a D(4)-quadruple for remaining cases.

diophantine m-tuples, pell equations

nije evidentirano