engleski

On the extension of D(-k)-pair {;k, k+1};

Let n be a nonzero integer. The set of m distinct positive integers is called D(n)-m-tuple, if the product of any of its two elements increased by n is a perfect square. In this talk we consider the problem of extending D(-k)-pair {;k, k+1};, where k is a positive integer. We prove the following result: Let k be a positive integer and {;k, k+1, c, d}; a D(-k)-quadruple with c>1. Then d=1.

Diophantine m-tuples

nije evidentirano