Solve for b in the given congruence, 2024 - 2023 ≡ b (mod 5).

The congruence given is:

\[
2024 - 2023 \equiv b \ (\text{mod} \ 5)
\]

First, simplify the left side:

\[
2024 - 2023 = 1
\]

So, the congruence becomes:

\[
1 \equiv b \ (\text{mod} \ 5)
\]

This means that \( b \) is the remainder when 1 is divided by 5. Since 1 divided by 5 gives a remainder of 1, we have:

\[
b = 1
\]

Thus, the solution is \( b = 1 \).

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you solve a general linear congruence equation of the form \( ax \equiv b \ (\text{mod} \ m) \)?
2. What is the significance of the modulus operation in number theory?
3. Can you solve \( 2023 \times 2024 \equiv x \ (\text{mod} \ 5) \)?
4. How does the Chinese Remainder Theorem help in solving systems of congruences?
5. What are the properties of modular arithmetic that are useful in solving congruences?

**Tip:** When solving congruences, reducing both sides of the equation modulo \( m \) can simplify the problem significantly.

Learn how to solve the congruence 2024 - 2023 ≡ b (mod 5) step-by-step. This problem involves modular arithmetic, specifically finding the remainder when 1 is divided by 5. Suitable for advanced high school students and beyond.

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