What is the remainder when is divided by 2024?
Logic Used:
Work modulo 2024. Note:
2023 ≡ −1 (mod 2024) and 2025 ≡ 1 (mod 2024).
Use parity of the exponent.
Solution:
2023²⁰²⁴ ≡ (−1)²⁰²⁴ = 1 (since 2024 is even).
2025²⁰²⁴ ≡ 1²⁰²⁴ = 1.
Sum ≡ 1 + 1 = 2 (mod 2024).
Correct Answer: 2
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