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.
2026-04-08 14:11:41.1775657501
Number of subfields of a given field
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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.