Answer: 8, and 8 divides it.
- A 8, and 8 divides it
- B 9, not divisible by 8
- C 3, not divisible by 8
- D 0, trivially special
Correct answer: A. 8, and 8 divides it
Explanation: 3²(1) − 1 = 9 − 1 = 8, which is divisible by 8.
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.