Let the set C = \ ( x, y ) ∣ x ^ 2 - 2 ^ y = 2023, x, y ∈ ℕ\ . Then...

Given

${x}^{2} - {2}^{y} = 2023$

$⇒ {x}^{2} = {2}^{y} + 2023$

Now, if $y = 1$ we get,

$⇒ {x}^{2} = 2025$

$⇒ x = 45$

And there is no other value which will satisfy the above equation,

Hence, $x = 45 \text{ and } y = 1$

So, $\mathop{∑}_{( x, y ) \in C} ( x + y ) = 45 + 1 = 46$