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Home » \( -5t^2 + 20t + 2 = 0 \) - Veritas Home Health

\( -5t^2 + 20t + 2 = 0 \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \(1 \cdot 2 \cdot 3 = 6\), which is not divisible by 12.

📌 Hence, 6 is the largest integer that must divide the product of any three consecutive integers.

📌 Question:** How many lattice points lie on the hyperbola \(x^2 - y^2 = 2024\) in the Cartesian plane?

📌 We seek integer solutions \((x, y)\) to the equation \(x^2 - y^2 = 2024\).

📌 This factors as:

📌 Let \(a = x - y\) and \(b = x + y\), so \(ab = 2024\), and \(x = \frac{a + b}{2}\), \(y = \frac{b - a}{2}\).

📌 For \(x\) and \(y\) to be integers, \(a + b\) and \(b - a\) must both be even, so \(a\) and \(b\) must have the same parity.

📌 Now factor 2024:

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