For which integers n is 2^8+2^11+2^n a perfect square?

Question

Hint: Let x^2=2^8+2^11+2^n, then try to factorize 2^n=2^8+2^11-x^2

Answer 1

I think this question would get a better response in the math section not the zoology section.

But the answer I get is 12.