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Home » Chase These Paldean Fates Cards: Ultimate Guide to Turning Your Luck Around! - Sterling Industries

Chase These Paldean Fates Cards: Ultimate Guide to Turning Your Luck Around! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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Since $ k $ must be a non-negative integer, valid values are $ k = 0,...
Thus, there are $ \boxed{14} $ integers between 1 and 100 that are con...
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} $.

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