Find the remainder when `5^(18)` is divided by 19.

Options

A. 1
B. 4
C. 11
D. 17

Explanation

To find the remainder when \(5^{18}\) is divided by 19, we can use Fermat's Little Theorem, which states that if \(p\) is a prime number and \(a\) is an integer not divisible by \(p\), then:

\[ a^{p-1} \equiv 1 \mod p \]

In this case, we have:
- \(a = 5\)
- \(p = 19\)

Since 5 is not divisible by 19, we can apply the theorem.

### Step 1: Identify \(p - 1\)
According to Fermat's Little Theorem, we need to calculate \(p - 1\):
\[ p - 1 = 19 - 1 = 18 \]

### Step 2: Apply Fermat's Little Theorem
Now, according to the theorem:
\[ 5^{18} \equiv 1 \mod 19 \]

This means that when \(5^{18}\) is divided by 19, the remainder is 1.

### Conclusion
Thus, the remainder when \(5^{18}\) is divided by 19 is:
\[ \boxed{1} \]