Galois Theory Through Exercises pp 177-234 | Cite as

# Examples and Selected Solutions

## Abstract

This chapters contains sample and in some cases complete solutions of some problems from Chaps. 1–15. We try to avoid solving standard problems formulated in these chapters, so that a solution is given as an example of how to handle similar problems to those presented in the text. Thus, the standard exercises in the text may be used as homework. Complete solutions to more special problems, as presented in this chapter, have at least three different functions. First, they contain a number of useful auxiliary results which are usually proved in the main texts of more standard textbooks. Second, some solutions are examples of how to work with the notions and approach similar problems (there is a rich selection of problems without solutions in Chap. 16). Third, some of the solutions presented in this chapter may be regarded as the last resort when serious attempts to solve a problem have been fruitless, or in order to compare one’s own solution to the one suggested in the book.

## References

- [LS]H.W. Lenstra and R.J. Schoof, Primitive normal bases for finite fields, Mathematics of Computation, 48 (1987), 217–231.MathSciNetCrossRefMATHGoogle Scholar