$$(2025)^{2025} - (2025)^{2024}$$​ is NOT divisible by

Correct option is B

Solution:

1. Simplify the Expression:

​$$2025^{2025} - 2025^{2024}$$

$$= 2025^{2024} \times (2025 - 1)$$

$$= 2025^{2024} \times 2024$$​​​

2. Factorize 2025 and 2024:

• 2025 = 3⁴ × 5² (no prime factors other than 3 and 5)

• 2024 = 2³ × 11 × 23

3. Check Divisibility:

• 8 (2³): Present in 2024 → Divisible

• 13: Not in 2025 or 2024 → Not divisible

• 23: Present in 2024 → Divisible

• 33 (3 × 11): 3 is in 2025, 11 is in 2024 → Divisible

Answer: B (13)is the correct option because 13 does not divide the expression.