Question

For all n ϵ N, 3.5^{2n + 1} + 23^{n + 1} is divisible by

A. 19
B. 17
C. 23
D. 25

Answer 1

B. 17

Given; P(n): 3.5^{2n + 1} + 2^{3n + 1}

⇒ P(1) = 3.5²⁺¹ + 2^{3 + 1} = 375 + 16 = 391 = 17 × 23

⇒ P(2) = 3.5⁴⁺¹ + 2⁶⁺¹ = 9375 + 256 = 9503 = 17 × 559

These are divisible by 17