When `(25)^26` is divided by 24, then the remainder will be?

Options

A. a)23
B. b)4
C. c)1
D. d)3

Answer

To find the remainder when \( 25^{26} \) is divided by \( 24 \), we can simplify the problem using modular arithmetic.

### Step-by-Step Solution:

1. **Understanding the Base**:
We start by rewriting \( 25 \) in terms of \( 24 \):
\[ 25 = 24 + 1 \]
This means that \( 25 \equiv 1 \mod 24 \).

2. **Applying the Exponent**:
Now, we raise both sides to the power of \( 26 \):
\[ 25^{26} \equiv 1^{26} \mod 24 \]

3. **Calculating the Power**:
Since \( 1^{26} = 1 \):
\[ 25^{26} \equiv 1 \mod 24 \]

4. **Finding the Remainder**:
This tells us that when \( 25^{26} \) is divided by \( 24 \), the remainder is:
\[ \text{Remainder} = 1 \]

### Final Answer:
The remainder when \( 25^{26} \) is divided by \( 24 \) is \( 1 \).