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Home » 20^3 = 8000 < 12000 - AMAZONAWS

20^3 = 8000 < 12000 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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A zoologist is studying the migratory patterns of a rare bird species....
To solve for \( n \) such that \( n^2 \equiv 1 \pmod{15} \), we start...
n^2 - 1 \equiv 0 \pmod{15} \implies (n-1)(n+1) \equiv 0 \pmod{15}
This means that \( (n-1)(n+1) \) is divisible by 15. Since 15 factors...
Step 1: Check modulo 3
The possible residues modulo 3 are 0, 1, and 2:
If \( n \equiv 0 \pmod{3} \), then \( n^2 \equiv 0 \pmod{3} \),
If \( n \equiv 1 \pmod{3} \), then \( n^2 \equiv 1 \pmod{3} \),
If \( n \equiv 2 \pmod{3} \), then \( n^2 \equiv 4 \equiv 1 \pmod{3} \...
Thus, \( n^2 \equiv 1 \pmod{3} \) when \( n \equiv 1 \) or \( 2 \pmod{...

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