Prooving by Pigeonhole principle
Let the $n$ distinct positive integers are represented by $c_1,\ldots,c_n$. Now form a series of sums as;

\begin{align}
S_1 =&amp;\; c_1 \\
S_2 =&amp;\; c_1 + c_2\\
    \vdots &amp; \\
S_n =&amp;\; c_1 + \ldots c_n
\end{align}

Now, use the pigeonhole principle on the $S_i$'s with $m$ holes and place them into the holes according to their result modulo $m$. We know that at least two $S_i$'s are sharing the same hole since $n&gt;m$. Let call them $S_i$ and $S_j$.

$S_i \equiv S_j \bmod m \implies S_j -S_i \equiv 0 \bmod m \implies m| S_j-S_i$ 

By using the definition of $S_i$ and $S_j$ we can say that if $i&lt;j$ then $m \;|\; a_{i+1} + \ldots + a_{j}$

if $n &lt;= m$ we cannot prove it and even we can find counterexamples.