Find the number of integers $n$ between $1$ and $2021$ such that $2^n+2^{n+3}$ is a perfect square.

parmenides51 wrote: Find the number of integers n between 1 and $2021 such that 2^n+2^{n+3} is a perfect square. Sorry for not writing in LATEX, but my acc isn't 2 weeks old yet. If someone could, please translate this. For a an integer, 2^n+2^{n+3}=a^2 9*2^n=a^2 Thus, n=2r, for any integer r. Thus 2^r=a/3 a=3*2^r, r=1,2..., 1005