The D(-k2)-triple {1,k2+1,k2+4} with k prime
Alan Filipin, Yasutsugu Fujita · Glasnik Matematicki · 2011
Let n be a nonzero integer.A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square.Let k be a prime number.In this paper we prove that the D(-k 2 )-triple {1, k 2 + 1, k 2 + 4} cannot be extended to a D(-k 2 )quadruple if k = 3.And for k = 3 we prove that if the set {1, 10, 13, d} is a D(-9)-quadruple, then d = 45.2010