  In 1988 P. Erd\"os asked if the prime divisors of $x^n -1$ for all $n=1,2,
>...$ determine the given integer $x$; the problem was affirmatively answered
by Corrales-Rodorig\'a\~nez and R. Schoof in 1997 together with its elliptic
version. Analogously, K. Yamanoi proved in 2004 that the support of the
pull-backed divisor $f^{*}D$ of an ample divisor on an abelian variety $A$ by
an algebraically non-degenerate entire holomorphic curve $f: \C \to A$
essentially determines the pair $(A, D)$. By making use of a recent theorem of
Noguchi-Winkelmann-Yamanoi in Nevanlinna theory, we here deal with this problem
for semi-abelian varieties: namely, given two polarized semi-abelian varieties
$(A_1, D_1)$, $(A_2,D_2)$ and entire non-degenerate holomorphic curves
$f_i:\C\to A_i$, $i=1,2$, we classify the cases when the inclusion $\supp
f_1^*D_1\subset \supp f_2^* D_2$ holds. We also apply a result of
Corvaja-Zannier on linear recurrence sequences to prove an arithmetic
counterpart.
