Time Machine Error -36

I have a NAS device attached to my router. I'm using it as a backup device for my Mac Book Pro. I'm getting the following error:

The backup disk image /Volumes/SHARE-1/MacBookPro.sparsebundle could not be created (error -36).

I'm not sure what the problem is. The NAS device is a Buffalo external device with a SMB (FAT) format. Could this be the problem?

Yes, the FAT is the problem. Time Machine needs an HFS+ formatted drive.

That's quite logical, since files copied from your HFS+ system have many attributes that could not be handled by the FAT filesystem, not even counting the files too long, or the characters that could not be accepted as a valid filename on FAT drives :)