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Let $F$ be a field with $5^{12}$ elements. What is the total number of proper subfields of $F$?

A) $3$ B) $6$ C) $8$ D) $5$

Explain the concept used to solve the question.

Alex M.
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vinoth
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1 Answers1

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$512=2^9$. So a subfield has $2^k$ elemet with $k\mid9$. What is the number of positive divisors of $9$?

If it is $5^{12}$. Then same. What is the number of positive divisors of $12$?

Moreover, since it say proper, we will get $-1$ of the above.

vudu vucu
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  • Sir i know this is old post but i have a doubt ! why k have to be divisor of 9 ? – RKK Jun 03 '22 at 05:58