Question

Find the natural number a for which Σf(a+k)(for k=1 to n) = 16(2ⁿ – 1), where the function f satisfies f (x + y) = f (x) . f (y) for all natural numbers x, y and further f (1) = 2.

Answer 1

Given that

and so on. Continuing the process, we obtain

But, we are given