Question

If P(n): “49ⁿ + 16ⁿ + k is divisible by 64 for n ∈ N” is true, then the least negative integral value of k is ______.

Answer 1

If P(n): “49ⁿ + 16ⁿ + k is divisible by 64 for n ∈ N” is true, then the least negative integral value of k is –1.

Explanation:

For n = 1,

P(1) : 65 + k is divisible by 64.

Thus k, should be –1

Since, 65 – 1 = 64 is divisible by 64.