The extendibility of D(4)-pair {;F_{;2k};, 5F_{;2k};};
Alan Filipin · The Fibonacci Quarterly · 2015
Let k ≥ 1 be an integer and let F_k be the k-th Fibonacci number. In this paper we prove that if {;F_{;2k};, 5F_{;2k};, c, d}; with c < d is the set of four positive integers such that any product of its two distinct elements increased by 4 is a perfect square, then d is uniquely determined by k and c.