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.
We relate the connection between the sizes of circuits in suborbital graph for the normalizer of in PSL(2,) and the congruence equations arising from related group action. We give a number theoretic result which says that all prime divisors of for any integer u must be congruent to .
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