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 $4=2^2$.

$2^8 + 2^{11} + 2^n = 2^8(1 + 8 + 2^{n-8})=2^8(9 + 2^{n-8})$
Therefore, $9 + 2^{n-8}$ has to be a perfect square. 
Clearly, $9 + 16 = 25$ is a perfect square. 
So, $2^{n-8} = 2^4$ giving, $$n = 12$$
