Beaver hunting/trapping/shooting

[Phill]

I have a question, I own some land directly down stream of crown land, every year beavers move in and cut down a few tree's then I trap or shoot them and feed them to the bears. Right up stream on the crown land is the "mother nest" a huge damn and beaver breeding grounds.... I'm pretty sure this is where I get my yearlings from...

These are pests in alberta... so what I'm wondering is, can I legally go on to the crown land, and shoot or trap the said beavers to hopefully limit my beaver problem? Is this breaking any laws??? Do I have to have a trappers license just to kill a pest on crown land?

Thanks