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do not go gentle into that good night interstellar - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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Question: What is the smallest positive integer $ n $ such that $ n^2...
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) \equi...
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 $.
The product is $ P = n(n+1)(n+2)(n+3) $.

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