Solutions to exercises from Marcus’ “Number Fields”


Marcus’ book “Number Fields” is famous for its great amount of exercises (303 to be precise, many of them splitting into sub-exercises), among which are also proofs of many major theorems (such as Kronecker-Weber theorem) and details necessary in future proofs (In Marcus’ own words, “[the] purpose of this is to make the proofs cleaner and easier to read, and to promote involvement on the part of the reader.”).

The exercises are structured in such a way that even during the first reading of the book the reader is able to solve all the problems, possibly refering to earlier exercises. However, to a reader encountering algebraic number theory for the first time, and probably also many who have only little background, many of these problems can cause trouble, which may cause a lot of inconvenience, especially given that these exercises often cover a major part of an argument further in the text.

It is very likely that a reader would like to, at this point, look up the solution to the exercise in order to proceed. Having a single file containing solutions to the exercises may come in very handy (I, personally, would very much appreciate having access to one during the reading of the book). With exactly this in mind, I have decided to compile a single file containing solutions to all the exercises in ths excellent book.

My hope is that this file will at some point help at least some people struggling with the exercises and will allow them to progress through the text.

If you have any questions or other feedback, please leave them as a comment below.

This file will be updated with every next chapter completed. So far, all exercises from chapters 1 and 2 are solved in the file.

I publish this book under CC BY-SA 4.0 license, so feel free to to share and redistribute. Once finished with the project, I plan on uploading the source files as well.


  1. Emi

    Sorry, can not find the file on this page.

    • Please click “Permalink” at the very top of the page, then on the next page click “Number Fields – solutions” link.

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