Induction 4 – Divisibility

You’ll learn

• Prove divisibility statements like 9ⁿ − 1 divisible by 8 with 4-step induction
• Split aᵏ⁺¹ as (1 + (a−1))·aᵏ so one piece matches the assumption, one holds the divisor
• Expand and group polynomials like (k+1)³ − (k+1) to expose the assumption
• Treat 'is divisible by' and 'is a factor of' as the same proof template