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gamer's guide pretty much everything - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \( 2^0 \cdot 3^2 \cdot 5^0 = 9 \)

📌 \( 2^2 \cdot 3^2 \cdot 5^0 = 4 \cdot 9 = 36 \)

📌 Sum: \( 1 + 4 + 9 + 36 = 50 \)

📌 Alternatively: sum = \( (1 + 2^2)(1 + 3^2)(1 + 5^0) \) but note: the general formula for sum of square divisors of \( n = \prod p^{e_i} \) is \( \prod \left( \sum_{k=0}^{\lfloor e_i/2 \rfloor} p^{2k} \right) \). Here, only up to \( c=0 \), so:

📌 Thus, the sum is \( \boxed{50} \).

📌 \boxed{50}

📌 Question: How many integer solutions \( (x, y) \) lie on the ellipse \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \) with \( |x| \leq 4 \) and \( |y| \leq 3 \)?

📌 The ellipse is \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \). Since \( |x| \leq 4 \), \( x^2 \leq 16 \), so \( \frac{x^2}{16} \leq 1 \), and similarly for \( y \).

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