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Some nuts are bad for dogs. Macadamia are a definite one to avoid. You also want to avoid too much salt or spice that can be on some nuts as well. Also chocolate covered nuts are bad because of the chocolate. Here is a website that talks about toxic foods to dogs.
A couple peanuts every now and then should be fine, but I wouldn't give a large amount of any kind of nuts to a dog.
Hope this info is helpful.