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Home » Why Quorra Tron Is Taking Over: The Latest Unfiltered Fact! 💥 - Aurero

Why Quorra Tron Is Taking Over: The Latest Unfiltered Fact! 💥 - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 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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\gcd(2^{10} - 1, 2^{15} - 1) = 2^5 - 1 = 32 - 1 = 31
The greatest common divisor is \(\boxed{31}\).
Question:** A zoologist tracking nocturnal animal activity cycles noti...
We seek the least three-digit number divisible by \( \text{lcm}(9, 12)...
First, compute the LCM:
= 3^2, \quad 12 = 2^2 \times 3 \quad \Rightarrow \quad \text{lcm}(9,12...
Now, find the smallest three-digit multiple of 36:
\left\lceil \frac{100}{36} \right\rceil = \left\lceil 2.777\ldots \rig...
So, the smallest such number is:
\times 3 = 108

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