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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) $. 📰 Confused Every Time About Hockey Periods Heres The Shocking Secret 2744964 📰 Golden Visa Usa 7894032 📰 I 275 Closure 7816007 📰 Calories Strawberries 5365664 📰 Big Bold Flavor In Every Bubbles Discover Fearless Flavored Sparkling Water 4171980 📰 Cant Find Your Outlook Help Number This Quick Guide Gets You Instant Aid 6834002 📰 Fxaix Yahoo Finance 7884941 📰 Wells Fargo 1800 Number 3621927 📰 Amm Airport 4297356 📰 Sumac Substitute 1676984 📰 Zombieville Usa What Happened When The Dead Went On The Rampage 9068404 📰 Archers Close To Me 3071092 📰 Dept For Health 9821074 📰 Effortless Elegance The Ultimate Green Dresses Every Woman Needs In Her Closet 1284623 📰 The Shocking Switch Price That Shook The Entire Industrydont Miss It 6780400