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Home » Thus, the number of integer coordinate points on the circle is: - Midis

Thus, the number of integer coordinate points on the circle is: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Solution: We are to find the smallest positive integer $ n $ such that:

📌 n^2 \equiv 1 \pmod{12}

📌 This implies $ n^2 - 1 \equiv 0 \pmod{12} $, or $ (n - 1)(n + 1) \equiv 0 \pmod{12} $.

📌 So $ 12 \mid (n - 1)(n + 1) $.

📌 We test small values of $ n $:

📌 $ n = 1 $: $ 1^2 = 1 \equiv 1 \pmod{12} $ ✅

📌 Thus, the smallest such $ n $ is $ \boxed{1} $.

📌 Solution: Consider four consecutive integers: $ n, n+1, n+2, n+3 $.

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