Given the equation: \(x^2 - 2^y = 2023\)
Step 1. By trial, we find that \( x = 45 \) and \( y = 1 \) satisfy the equation, as:
\(45^2 - 2^1 = 2025 - 2 = 2023\)
Step 2. Thus, the only solution in \( C \) is \( (x, y) = (45, 1) \).
Step 3. Calculate \( \sum_{(x, y) \in C} (x + y) \):
\(\sum_{(x, y) \in C} (x + y) = 45 + 1 = 46\)
The Correct Answer is: 46
Let \( S = \{p_1, p_2, \dots, p_{10}\} \) be the set of the first ten prime numbers. Let \( A = S \cup P \), where \( P \) is the set of all possible products of distinct elements of \( S \). Then the number of all ordered pairs \( (x, y) \), where \( x \in S \), \( y \in A \), and \( x \) divides \( y \), is _________.