According to PublishingBasics.com, the answer is yes. With an asterisk.

This is probably one of the most asked; least understood questions out there in the self-publishing world today. Technically you not only need an ISBN but you need a different ISBN for each format your ebook is being offered. If you are offering your book as a mobi, epub and a PDF, you need three different ISBNs. That’s technically. In reality, if you are only making your eBook available on Amazon, you don’t need any. Confused? Read the entire piece.

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