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a large population of land turtles on an isolated island - Anadea

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: How many lattice points lie on the hyperbola $

📌 Solution: A lattice point is a point with integer coordinates. The hyperbola is given by:

📌 Multiply both sides by $ 400 $ (LCM of 25 and 16) to eliminate denominators:

📌 We now look for integer solutions $ (x, y) $ to this equation. Rearranging:

📌 So $ (5, 0), (-5, 0) $ are solutions.

📌 Try $ d = 25 $: $ x + y = 40 $, many such pairs.

📌 Try $ d = 20 $: $ x + y = 50 $, many such pairs.

📌 Try $ d = 10 $: $ x + y = 100 $, many such pairs.

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