  A prime number $p$ is called a Schenker prime if there exists such
$n\in\mathbb{N}_+$ that $p\nmid n$ and $p\mid a_n$, where $a_n =
\sum_{j=0}^{n}\frac{n!}{j!}n^j$ is so-called Schenker sum. T. Amdeberhan, D.
Callan and V. Moll formulated two conjectures concerning $p$-adic valuations of
$a_n$ in case when $p$ is a Schenker prime. In particular, they asked whether
for each $k\in\mathbb{N}_+$ there exists the unique positive integer $n_k<p^k$
such that $v_p(a_{m\cdot 5^k + n_k})\geq k$ for each nonnegative integer $m$.
We prove that for every $k\in\mathbb{N}_+$ the inequality $v_5(a_n)\geq k$ has
exactly one solution modulo $5^k$. This confirms the first conjecture stated by
the mentioned authors. Moreover, we show that if $37\nmid n$ then
$v_{37}(a_n)\leq 1$, what means that the second conjecture stated by the
mentioned authors is not true.
