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Home » Solution: The average of the four times is given by: - Dyverse

Solution: The average of the four times is given by: - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\( n \equiv 1 \pmod{5} \Rightarrow n^2 \equiv 1 \pmod{5} \),
\( n \equiv 2 \pmod{5} \Rightarrow n^2 \equiv 4 \pmod{5} \),
\( n \equiv 3 \pmod{5} \Rightarrow n^2 \equiv 9 \equiv 4 \pmod{5} \),
\( n \equiv 4 \pmod{5} \Rightarrow n^2 \equiv 16 \equiv 1 \pmod{5} \).
So, \( n^2 \equiv 1 \pmod{5} \) when \( n \equiv 1 \) or \( 4 \pmod{5}...
Step 3: Combine using Chinese Remainder Theorem
We seek the smallest positive \( n \) such that:
\( n \equiv 1 \text{ or } 2 \pmod{3} \)
\( n \equiv 1 \text{ or } 4 \pmod{5} \)
\( n \equiv 1 \pmod{3}, n \equiv 1 \pmod{5} \Rightarrow n \equiv 1 \pm...

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