Question

For all n ∈ N, 3 × 5^{2n + 1} + 2^{3n + 1} is divisible by 

A. 19 

B. 17 

C. 23 

D. 25

Answer 1

Given for all n€ N 3 × 5²ⁿ⁺¹ + 2³ⁿ⁺¹ 

For n=1, 

3 × 5³ + 2⁴ 

3 × 125 + 16 

375 + 16 = 391 

For n=2, 

3 × 5⁵ + 2⁷ 

3 × 3125 +128 

9375 + 128 = 9503 

H.C.F of 391, 9503 = 17