Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Suppose you wish to prove the statement that follows using the extended principle of mathematical is 2 is a factor of $5 ^ { n } - 3$ , for all natural numbers $n$ .
Assume that $S _ { k }$ is true for $\mathrm { k } \geq 1$ where $S _ { k }$ is the statement that 2 is a factor of $5 ^ { k } - 3$ , and write the statement $S _ { k + 1 }$ .

A) $S _ { k + 1 } : 2$ is a factor of $5 ^ { k + 1 } - 3$ .
B) $S _ { k + 1 } : 2$ is a factor of $6 ^ { k + 1 } - 3$ .
C) $S _ { k + 1 } : 2$ is a factor of $6 ^ { k } - 3$ .
D) $S _ { k + 1 } : 2$ is a factor of $5 ^ { k } - 2$ . ion.