Is $\mathbb F_p$ the set of all non-zero elements of $\mathbb Z_p$?
Also I have a confusion in the number of elements of $(\mathbb F_p)^3=\mathbb F_p \oplus \mathbb F_p\oplus\mathbb F_p$. What will be the number of elements of this set.
Please someone help.
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$\begingroup$I assume that $p$ is a prime number.
Then $\mathbb F_p$ and $\mathbb Z_p$ both denote the set of classes of integers mod $p$.
The notation $\mathbb F_p$ is typically used when the emphasis is on the fact that it is a field: $\mathbb F_p$ is the finite field with $p$ elements.
The underlying set in $(\mathbb F_p)^3=\mathbb F_p \oplus \mathbb F_p\oplus\mathbb F_p$ is the Cartesian product of three copies of $\mathbb F_p$. Now consider this: if $A$ is a set with $n$ elements, how many elements are there in the set $A \times A \times A$ ?
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