Dr. Fred, following a messy divorce, has encountered significant financial difficulties. Dr. Fred has a friend named Slick Slim who tells Dr. Fred that he has been making lots of money by selling people a wristband that allegedly places pressure on a nerve that signals hunger resulting in a lack of appetite. Slick Slim tells Dr. Fred that, although the device does not really work, people who want to lose weight and look good in their bathing suits will do anything and that it sells like hotcakes. Slick Slim tells Dr. Fred that he will pay Dr. Fred five dollars for every band that Dr. Fred can sell to his patients. Dr. Fred proceeds to mail letters to patients suggesting the use of the band for weight loss. He also uses UPS to mail samples of the band to some patients along with letters encouraging purchase of the bands. Dr. Fred then proceeds to bill Medicare for office consultations he has with patients when they come in to purchase the bands. The scheme is wildly successful. Dr. Fred is able to entirely satisfy his alimony obligations within just a few months. Unfortunately, as patients begin to see that they are not having any weight loss, he has been receiving numerous complaints, and a friend of his told him that he could even be facing some criminal prosecution. By mailing correspondence to patients encouraging purchase of the band, which of the following offenses, if any, did Dr. Fred commit?