Divisibility of Linear Combinations
Prove that
\[
a \mid \sum_{i=1}^{n} b_i c_i
\]
given that
\[
a \mid b_i \qquad \text{for all } i=1,2,\ldots,n,
\]
where $a,b_i,c_i$ are integers and $n$ is a positive integer.
Prove that
\[
a \mid \sum_{i=1}^{n} b_i c_i
\]
given that
\[
a \mid b_i \qquad \text{for all } i=1,2,\ldots,n,
\]
where $a,b_i,c_i$ are integers and $n$ is a positive integer.