Find all natural numbers n to make 2007 + 4 ^ n square

Find all natural numbers n to make 2007 + 4 ^ n square

Such natural numbers do not exist
Note the square of the natural number: the square of the even number divided by 4, the remainder is 0, and the odd number gets the square divided by 4, the remainder is 1. It can be seen that the square divided by 4 is more than 1 or 0. In the original problem, when n is positive, the remainder divided by 4 is always 3, which can not be a square number. When n = 0, the power of the prime factor in 2008 is odd (for example, the power of 2 is 3), which is not a square number
I hope my answer can help you!