Goodreads Librarians Group discussion
Book & Author Page Issues
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ISBN Confusion... Please Help!
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If you do do that, however, you should put a Librarian's Note: in the description area about the ISBN problem and listing the ISBNs given in the book. That way the ISBN info will at least be available and others will be able to understand the issue.
The other possibility (and given that this book is from a small publisher, I'm betting on this one) is that the PUBLISHER messed up, and assigned the book non-corresponding ISBNs.
(You can convert between ISBN-10s and ISBN-13s using tools like this.)