The image shows a question written in Russian, asking to "Choose a simple field from the list." The options are:

1. $\mathbb{Z}_p$, the ring of residues modulo $p$, where $p$ is a prime number.
2. The field of real numbers $\mathbb{R}$.
3. The field of complex numbers $\mathbb{C}$.

Correct Answer:

The correct answer is $\mathbb{Z}_p$, where $p$ is a prime number, as it forms a finite field (also known as a Galois field) when $p$ is prime.

Would you like an explanation of why this is the case, or more examples of fields?

Here are 5 related questions for practice:

1. What properties make $\mathbb{Z}_p$ a field when $p$ is a prime number?
2. What distinguishes a field from a ring?
3. Can $\mathbb{R}$ or $\mathbb{C}$ be considered simple fields? Why or why not?
4. What is the definition of a finite field?
5. How does $\mathbb{Z}_p$ behave if $p$ is not a prime number?

Tip: Remember that a field must satisfy two operations (addition and multiplication) with inverses for all nonzero elements.