maths question very difficult?

Question

any help would be great ,even if explaining a good way to do it.

here it is:
R = 4 to the power of 40 + 4 to the power of 1024 + 4 to the power of H.
What is the the largest number H can be so that R is the square of a whole number?

H and R are whole numbers.

Answer 1

This problem pops up now and then. Here's a recipe:

1) What would a binomial have to look like to get a square
with three powers of 4?

2) Use the form to get the answer 2007

3) prove that for any H>2007 , the number is not square,
it lies between consecutive squares.