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Home » Discover Your Perfect Name + Place: Unlock Your Unique Identity with Our Genius Generator! - AMAZONAWS

Discover Your Perfect Name + Place: Unlock Your Unique Identity with Our Genius Generator! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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🔥 Popular Posts

Question: How many lattice points lie on the hyperbola $x^2 - 4y^2 = 1...
Solution: Rewrite as $x^2 = 4y^2 + 100$. Let $x = 2k$, then $4k^2 = 4y...
For $(1,25)$: $k - y = 1$, $k + y = 25$ → $k = 13$, $y = 12$ → $x = 26...
For $(5,5)$: $k - y = 5$, $k + y = 5$ → $k = 5$, $y = 0$ → $x = 10$.
Negative pairs yield symmetric solutions. Total lattice points: $(\pm2...
Solution: We are given a recurrence:
T(1) = 4, \quad T(n) = 2T(n-1) + 3 \text{ for } n \geq 2.
We compute $ T(n) $ for $ n = 1 $ to $ 5 $:
$ T(1) = 4 $
$ T(2) = 2 \cdot 4 + 3 = 8 + 3 = 11 $

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