Let the set $C=\left{(x, y) \mid x^{2}-2^{y}=2023, x, y \in \mathbb{N}\right}$. Then $\sum_{(x, y)=C}(x+y)$ is equal to
$x^{2}-2^{y}=2023$
$\Rightarrow x=45, y=1$
$\sum_{(x, y)=C}(x+y)=46$.
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