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Home » Number of doubling periods = 18 ÷ 3 = 6 - Portal da AcÃºstica

Number of doubling periods = 18 ÷ 3 = 6 - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 This represents an ellipse centered at the origin with semi-major axis \(a = 3\) and semi-minor axis \(b = 2\).

📌 We need to find integer solutions \((x, y)\) \((x, y) \in \mathbb{Z}^2\) that lie on the ellipse.

📌 Since \(x^2 \leq 9\), possible integer values for \(x\) are \(x = -3, -2, -1, 0, 1, 2, 3\).

📌 Similarly, \(y^2 \leq 4\), so integer values for \(y\) are \(y = -2, -1, 0, 1, 2\).

📌 We test each pair \((x, y)\) to see if it satisfies the equation.

📌 \(x = 0\):

📌 rac{0}{9} + rac{y^2}{4} = 1 \Rightarrow y^2 = 4 \Rightarrow y = \pm 2

📌 Points: \((0, 2), (0, -2)\)

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