If n is any positive integer, then (3⁴ – 4³ⁿ) is always divisible by ______ .

Explanation

Let, n = 1, 2, 3, ...... If n = 1 Then, 3⁴ⁿ – 4³ⁿ = 3⁴ – 4³ If n = 2 ⇒ 81 – 64 = 17 Then, 3⁸ – 4⁶ = 3⁴ × 3⁴ – 4³ × 4³ = 81 × 81 – 64 × 64 = (81 + 64) (81 – 64) = 145 × 17 ∵ If n is any positive integer then 3⁴ⁿ – 4³ⁿ is divisibal by 17.