Hello there!
Pasty butt is very common. They say that if a chick is a little bit chilly, that is a cause of pasty butt, but I don't think that's truly the cause. It seems I always have one chick with pasty butt, but usually that's when they're under a week old. I clean that off in some warm water, and then I blow dry their butts because a naked butt often looks red and the other chicks will be attracted to that, then you end up with chicks with bald sore bottoms.
A friend of mine shared a little trick she uses, and it truly works. If you can go outside, and dig up a clump of grass with the roots and dirt still attached, and put that into your brooder. The chicks will just go bananas over this, and they'll eat the grass and they'll also eat some of the dirt, they'll play on it and scratch on it.......(This is what they would naturally do if they were outside with their mother.) Anyhow, do that once a day if you are able, and you won't have anymore pasty butt. Just be particular where you dig up your clump.....Don't dig up the grass clump in an area where other pets or chickens have been pooping....Pick a fresh spot. This truly works like a charm.
It's kind of unusual for week old chicks to have pasty but (in my experience), so you might want to just make sure they're warm enough.......
Good luck to you!
Sharon