Make $2^8 + 2^{11} + 2^n$ a perfect square Can someone help me with this exercise? I tried to do it, but it was very hard to solve it. 
Find the value of $n$ to make $2^8 + 2^{11} + 2^n$ a perfect square.
It is the same thing like $4=2^2$.

You can write
$$2^8+2^{11}+2^n=(2^4)^2+2.2^4.2^6+2^n$$
now, note that if $n=12$, follows that
$$(2^4)^2+2.2^4.2^6+2^{12}=(2^4)^2+2.2^4.2^6+(2^6)^2=(2^4+2^6)^2$$
Thus, $n=12$ to solve the problem.
