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Let F be a field of order 2n. Prove that char F = 2.

Chapter 13, Problem 35E

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QUESTION:

Let F be a field of order 2n. Prove that char F = 2.

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QUESTION:

Let F be a field of order 2n. Prove that char F = 2.

ANSWER:

Step 1 of 2

Let us consider a field F of order .

It is known that any field is an integral domain. Therefore, the characteristic of F is only a prime number.

We also know that the characteristic is equal to the order of 1.

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