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Home » Divide by \(-2\) (note that dividing by a negative reverses the inequality): - Simpleprint

Divide by \(-2\) (note that dividing by a negative reverses the inequality): - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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Dividing by 7:
-\frac{2}{7} \leq k \leq \frac{97}{7} \approx 13.857
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 $:

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