How to find collisions in a hash function knowing its coefficent?
We can easily find collisions for this system.

Let $x=(x_1,...,x_n) $ be a sequence such that $h(x)=k$. For finding collision we can do this:

Select $x'=(x_1',...,x_{n-1}')$ and then compute:


  $$x_n'=({a_n}^{-1}\cdot(k-\sum_{i=1}^{n-1}a_ix_i')) \bmod N$$


Now we have  $h(x)=h(x')=k$.