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## Main Question or Discussion Point

Hi, I am taking a class in Linear Algebra II as a breadth requirement. I have not studied Algebra in a formal class, unlike 95% of the rest of the class (math majors). My LA2 professor mentioned the following fact in class:

"The number of elements of a finite field is always a prime power and conversely, every prime power occurs as the number of elements in some finite field (which is unique up to isomorphism)."

The exact words are Wikipedia's but that's about what the Prof said.

I only vaguely understand the concept of rings, fields and groups. I cannot understand why the number of elements in a finite field is a power of primes.

"The number of elements of a finite field is always a prime power and conversely, every prime power occurs as the number of elements in some finite field (which is unique up to isomorphism)."

The exact words are Wikipedia's but that's about what the Prof said.

I only vaguely understand the concept of rings, fields and groups. I cannot understand why the number of elements in a finite field is a power of primes.