Q. 2

# Mark the Correct alternative in the following:

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

A. 19

B. 17

C. 23

D. 25

Answer :

Given for all n€ N 3 × 5^{2n+1} + 2^{3n+1}

For n=1,

3 × 5^{3} + 2^{4}

3 × 125 + 16

375 + 16 = 391

For n=2,

3 × 5^{5} + 2^{7}

3 × 3125 +128

9375 + 128 = 9503

H.C.F of 391, 9503 = 17

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