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Home » x^2 + y^2 = 5200 - Midis

x^2 + y^2 = 5200 - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\( x = \pm 1 \): \( 9(1) = 9 \Rightarrow 25y^2 = 216 \Rightarrow y^2 =...
\( x = \pm 2 \): \( 9(4) = 36 \Rightarrow 25y^2 = 189 \Rightarrow y^2...
\( x = \pm 3 \): \( 9(9) = 81 \Rightarrow 25y^2 = 144 \Rightarrow y^2...
\( x = \pm 4 \): \( 9(16) = 144 \Rightarrow 25y^2 = 81 \Rightarrow y^2...
\( x = \pm 5 \): \( 9(25) = 225 \Rightarrow 25y^2 = 0 \Rightarrow y =...
Total lattice points: \( (0, \pm3), (\pm5, 0) \) → 4 points.
Thus, the number of lattice points is \( \boxed{4} \).
Question:** How many of the 150 smallest positive integers are congrue...
Solution:** We want integers \( n \) such that \( 1 \leq n \leq 150 \)...
Such numbers are of the form \( n = 7k + 3 \).

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