engleski

The extension of D(-k^2)-triple {;1, k^2 + 1, k^2 + 4}; with k prime

Let n <> 0 be an integer. A set of m positive distinct integers is called a 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 extension of D(-k^2)-triple {;1 k^2 + 1, k^2 + 4}; with k prime and we prove that this triple cannot be extended to a quadruple if k > 3, and if k = 3, we show that D(-9)-triple {;1, 10, 13}; has a unique extension to the D(-9)-quadruple {;1, 10, 13, 45};.

diophantine m-tuples

nije evidentirano