21) What is the unit digit of $17^{17}$?
(A) 1,
(B) 3,
(C) 5,
(D) 7,
(E) 9.
21. The answer is $(\mathbf{D})$.

The unit digit of a product is determined only by the product of the unit digits of the factors. Therefore:

$17^{2}$ has the same unit digit as $7 \times 7$, which is 9;

$17^{3}$ has the same unit digit as $9 \times 7$, which is 3;

$17^{4}$ has the same unit digit as $3 \times 7$, which is 1;

$17^{5}$ has the same unit digit as $1 \times 7$, which is 7, or the same unit digit as $17^{1}$.

The unit digit of the powers of 17 thus repeats every 4 consecutive values of the exponent.

Since $17=4 \cdot 4+1$, the unit digit of $17^{17}$ is the same as $17^{1}$, which is 7.