AMC 12 2020b Problem 21

How many positive integers $n$ satisfy$$\frac{n+1000}{70} = \lfloor \sqrt{n} \rfloor?$$(Recall that $\lfloor x\rfloor$ is the greatest integer not exceeding $x$.)

$\textbf{(A) } 2 \textbf{(B) } 4 \textbf{(C) } 6 \textbf{(D) } 30 \textbf{(E) } 32$