Disconnectedness of the subgraph F-3 for the group Gamma(3)

Abstract

In this paper we show that the subgraph F-3 is disconnected and that for all integers m, we find all integers a and b such that (9m(2) - 4)a(2) + 4 and 5b(2) +/- 4 are square. It turns out that the set of numbers b comprises the Fibonacci numbers.