Answer: 4.
- A 2
- B 3
- C 4
- D 5
Correct answer: C. 4
Explanation: 7ⁿ − 3ⁿ is divisible by 7 − 3 = 4 for all positive integers n.
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.