Perfect square involving the exponential law If $n$ is a natural number, and $2^{10} + 2^{13} + 2^n$ is a perfect square, what is the value of $n$?
I've attempted to factor out $2^{10}$ and got $2^{10}(1 + 2^3 + 2^{n-10})$. How can I move further?

We can factor out the $2^{10}$ first:
$$2^{10}(1+2^3+2^{n−10})$$
We can simplify $2^3 = 2\cdot{2}\cdot{2} = 8$. Also, because $2^{10}$ is a perfect square, we can remove it from the equation.
$$1+8+2^{n-10}=9+2^{n-10}$$
Now we can add a new variable, $m$, where $m$ can be any positive integer. We can rewrite our equation as:
$$9+2^{n-10}=m^2$$
We can now test values for $n-10$. If we do this, we'll find that $9 + 2^4 = 9+16=25=5^2$.
So $n-10=4$, and $n=14.$
