How is this type of polynomial $\prod_{i=1}^N (x-i)$ called?

Question

How is this type of polynomial $\prod_{i}^N (x-i)$ called? $N$ is an arbitrary integer.

Is there a well-known property? It would be nice to get to know that.

Answer 1

It is the unique monic polynomial wih degree $N$ and exactly $N$ integer roots $x=1,2,\ldots,N$.