If `P(n): 49^n+16^n+lambda` is divisible by 64 for `n in N` is true, then the least negative integral value of `lambda` is

Options

A. `- 3`
B. `- 2`
C. `- 1`
D. `- 4`

Answer

C

Explanation

For `n=1`, we have

`49n
+16n+λ=49+16+λ=65+λ=64+(λ+1)`,
Which is divisible by `64` if `λ=−1.`

For n=2, we have
`49n+16n+λ=492+16×2+λ=2433+λ=(64×38)+(λ+1)`,
which is divisible by ` 64` if `λ=−1`

Hence, `λ=−1.`