In 1970, Kotzig and Rosa defined the concept of edge-magic labelings as follows. Let
$G$
be a simple
$\left( p,\,q \right)$
-graph (that is, a graph of order
$p$
and size
$q$
without loops or multiple edges). A bijective function
$f:\,V\left( G \right)\cup E\left( G \right)\,\to \,\left\{ 1,\,2,\,.\,.\,.\,,\,p\,+\,q \right\}$
is an edge-magic labeling of
$G$
if
$f\left( u \right)\,+\,f\left( uv \right)\,+f\left( v \right)\,=\,k$
, for all
$uv\,\in \,E\left( G \right)$
. A graph that admits an edge-magic labeling is called an edge-magic graph, and
$k$
is called the magic sum of the labeling. An old conjecture of Godbold and Slater states that all possible theoretical magic sums are attained for each cycle of order
$n\,\ge \,7$
. Motivated by this conjecture, we prove that for all
${{n}_{0}}\,\in \,\mathbb{N}$
, there exists
$n\,\in \,\mathbb{N}$
such that the cycle
${{C}_{n}}$
admits at least
${{n}_{0}}$
edge-magic labelings with at least
${{n}_{0}}$
mutually distinct magic sums. We do this by providing a lower bound for the number of magic sums of the cycle
${{C}_{n}}$
, depending on the sum of the exponents of the odd primes appearing in the prime factorization of
$n$
.