Suppose there is an integer $N$ and I want to count the number of $a$s that $a^2 \mathop\equiv\limits^{N} b $,
when $b \in I$ for certain interval $I$ and $N$ goes to infinity.
is it almost trivial?
for example if $I= [-\frac{N \delta}{2},\frac{N \delta}{2}]$, Is the answer $|I| + O(1)$ ?