CoCalc -- finite.ipynb

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Finite fields appear in many applications of algebra, including coding theory and cryptography. We already know one finite field, ${\mathbb Z}_p\text{,}$ where $p$ is prime. In this chapter we will show that a unique finite field of order $p^n$ exists for every prime $p\text{,}$ where $n$ is a positive integer. Finite fields are also called Galois fields in honor of Évariste Galois, who was one of the first mathematicians to investigate them.

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