It seems like you are asking how to calculate $2025 \mod 2025$, which is a modular arithmetic operation.

To solve this:

General Rule for Modulo:

The modulus operation $a \mod m$ returns the remainder when $a$ is divided by $m$.

In your case, $a = 2025$ and $m = 2025$.

Calculation:

$2025 \mod 2025 = 2025 - \left\lfloor \frac{2025}{2025} \right\rfloor \times 2025$

Since $\frac{2025}{2025} = 1$, we have:

$2025 \mod 2025 = 2025 - (1 \times 2025) = 2025 - 2025 = 0$

Conclusion:

$2025 \mod 2025 = 0$

Would you like further details on modular arithmetic? Here are some related questions:

1. What is the significance of modular arithmetic in number theory?
2. How do modular exponentiation and its properties work?
3. How does one solve large powers in modular arithmetic, like $2025^{2025} \mod 2025$?
4. Can we apply the Chinese Remainder Theorem in modular arithmetic?
5. How are negative numbers treated in modular arithmetic?

Tip: Modular arithmetic is particularly useful when working with large numbers, such as in cryptography, as it simplifies calculations by reducing the size of the numbers you need to work with.