The set of $m$ positive integers with the property that the product of any two of them increased by $4$ is a perfect square is called a $D(4)$-$m$-tuple. In this paper we consider the extensibility of general $D(4)$-pair $\{a,b\}$ and prove some results that support the conjecture that there does not exist a $D(4)$-quintuple.
Publié le : 2013-11-12
Classification:
Diphantine tuples, system of Diophantine equations,
11D09, 11J68
@article{mc142,
author = {Ba\'ci\'c, Ljubica and Filipin, Alan},
title = {The extendibility of $D(4)$-pairs},
journal = {Mathematical Communications},
volume = {18},
number = {1},
year = {2013},
pages = { 447-456},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc142}
}
Baćić, Ljubica; Filipin, Alan. The extendibility of $D(4)$-pairs. Mathematical Communications, Tome 18 (2013) no. 1, pp. 447-456. http://gdmltest.u-ga.fr/item/mc142/