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📰 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: $(\pm26, \pm12)$ and $(\pm10, 0)$, totaling $\boxed{6}$.Question: A mechanical engineer is designing a gear system where the torque output $ T(n) $ at segment $ n $ is defined recursively by $ T(n) = 2T(n-1) + 3 $, with $ T(1) = 4 $. If the system evaluates $ T(m) $ for a specific $ m $, and the sum $ S(m) = \sum_{n=1}^{m} T(n) $ models total energy over time, compute $ S(5) $. 📰 This Simple Textarea Hack Will Transform Your Website Experience Ultimate Pro Tip 3465891 📰 Human Resource Management System 5874871 📰 This Live Attenuated Vaccine Could Be Your Best Defense Against Devastating Diseases 8791279 📰 Hotels In Midland Tx 1911584 📰 Faster Way To Fat Loss Reviews 8783618 📰 Your Wall Just Just Became A Goal Machine Amazing Football Wallpapers You Need 137333 📰 Lost In The Desert Roblox 1488156 📰 Get A Free Iphone 8819350 📰 Credit Scores 7257741 📰 Young Demi Moore 5148757 📰 Pirate Games 6399453 📰 Hhs Us Vs The Nation How One Agency Is Revolutionizing Healthcare Like Never Before 8890270 📰 Youll Never Guess This Magnetic Knife Holder Stays Sharp And Perfect Every Day 7632799 📰 This Viral Moment With Riley Andersen Will Change How You View Her Forever 5259249 📰 Why Everyones Talking About The Castle Of Illusionyou Need To See It 182867