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Home » Why Everyone’s Raving Over This Realistic Barn Drawing Everyone’s Been Missing! - Upplift

Why Everyone’s Raving Over This Realistic Barn Drawing Everyone’s Been Missing! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 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 $.

🔥 Popular Posts

C \approx 8 \times 3.14 = 25.12
#### 25.12
A sequence is defined by \( a_n = 3n^2 - 2n + 1 \). Find the sum of th...
a_1 = 3(1)^2 - 2(1) + 1 = 2
a_2 = 3(2)^2 - 2(2) + 1 = 9
a_3 = 3(3)^2 - 2(3) + 1 = 22
a_4 = 3(4)^2 - 2(4) + 1 = 41
a_5 = 3(5)^2 - 2(5) + 1 = 66
Sum of the first 5 terms:
+ 9 + 22 + 41 + 66 = 140

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