Question

What is the remainder when (225)²²⁵ is divided by 14?

• A. 1
• B. 3
• C. 5
• D. 7

Answer 1

The Correct Option is A

Finding the Remainder Using Fermat’s Theorem

Step 1: Compute $225 \mod 14$

We first divide 225 by 14:

$$225 \div 14 = 16 \text{ remainder } 1$$

Thus,

$$225 \equiv 1 \mod 14$$

Step 2: Apply Exponentiation

Since any power of 1 remains 1, we have:

$$225^{225} \equiv 1^{225} \equiv 1 \mod 14$$ 

Final Answer:

Thus, the remainder is 1 (Option A).