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).