Question

How many pairs (m,n) of integers satisfy the equation 4^m = n^2 + 15?

Answer 1

M = 2; N = 1

15 can be written as product of 3 and 5.

i.e. 15 = (4-1) * (4+1) = (4² - 1²)

or, 4² = 1² + 15

Now comparing it with 4^m=n^2+15 we get,

m = 2; n = 1.

But this isn't the answer.

You've to find out the number of possible combinations out of this.

Thuis we have only two options:

64 - 49 = 15 and 16 - 1 = 15.

So, two possible combinations, where (m,n) = (3,7) & (2,1) [4³=64]