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Home » C = \pi \cdot d = \pi \cdot 8\sqrt2 = 8\sqrt2\pi \text cm. - ClickBalance

C = \pi \cdot d = \pi \cdot 8\sqrt2 = 8\sqrt2\pi \text cm. - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 \( 1005 \equiv 4 \)

📌 \( 1007 \equiv 6 \)

📌 \( 1009 \equiv 8 \)

📌 Sum: \( 0 + 2 + 4 + 6 + 8 = 20 \), and \( 20 \mod 11 = 9 \).

📌 Thus, the remainder is \( \boxed{9} \).

📌 Question:** How many lattice points lie on the ellipse \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \)?

📌 Solution:** We seek integer solutions \( (x, y) \) to \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \), or equivalently:

📌 9x^2 + 25y^2 = 225

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