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Home » Case 2: \( b - 3 = -5 \Rightarrow b = -2 \) - Deep Underground Poetry

Case 2: \( b - 3 = -5 \Rightarrow b = -2 \) - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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First, observe $3^1 = 3$, $3^2 = 9 \equiv 1 \pmod{8}$, so the powers o...
Since $2025$ is odd, $3^{2025} \equiv 3 \pmod{8}$.
Next, $5^1 = 5$, $5^2 = 25 \equiv 1 \pmod{8}$, so powers of 5 mod 8 al...
$2025$ is odd, so $5^{2025} \equiv 5 \pmod{8}$.
Add: $3 + 5 = 8 \equiv 0 \pmod{8}$.
Question: A paleontologist dates a fossil using a sequence of radiomet...
Solution: We seek the smallest $n > 0$ such that $2^n \equiv 12 \pmod{...
Compute successive powers of 2 modulo 25:
$2^1 = 2$
$2^2 = 4$

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