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49ⁿ + 16n + k is divisible by 64 for n ∈ N. Then the numerically least-ve integral value of k is

A. -2

B. -1

C. -3

D. -4

E. None of the above

View Answer

Correct choice: C

Explanation:

49n + 16n + k is divisible by 64 and k is the least –ve integer.
⇒49 + 16 + k is divisible by 64
⇒65 + k is divisible by 64
⇒k = –1.

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