Suppose that
,
where
is an odd positive integer. First, an infinite digraph
is defined, where the
vertex set is
and the edge
set is
. Then the following
results are proved: if
,
then the digraph
is
weakly connected; if
is
a safe prime, i.e., both
and
are primes,
then the number
of weakly connected components of the digraph
is 2. Finally, a conjecture that there are infinitely many primes
such
that
is presented.
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