To solve the expression \( 5^{40} \div 4 \) and find the remainder:

### Step-by-Step Solution:
1. The goal is to find the remainder when \( 5^{40} \) is divided by 4.
2. Since \( 5 \equiv 1 \pmod{4} \), this means \( 5^n \equiv 1^n \pmod{4} \) for any integer \( n \).
3. Therefore, \( 5^{40} \equiv 1^{40} \equiv 1 \

Find the remainder when solving 5^40 divided by 4 using modular arithmetic. This problem uses properties of exponentiation and modular arithmetic to simplify the calculation, and is suitable for students in Grades 10-12.

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