The remainder when `(16)^3500` is divided by 17 is

Options

A. 1
B. 0
C. 16
D. none

Explanation

To find the remainder when \( 16^{3500} \) is divided by 17, 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:

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

In this case, we have \( a = 16 \) and \( p = 17 \).

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