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Home » \[ a^2 + b^2 = c^2 = 100 \] - go-checkin.com

\[ a^2 + b^2 = c^2 = 100 \] - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \( 2^3 = 0 \)

📌 \( 4^3 = 64 \equiv 0 \)

📌 \( 6^3 = 216 \equiv 0 \)

📌 So only \( n \equiv 1 \pmod{8} \) gives \( n^3 \equiv 1 \). So we require:

📌 n \equiv 1 \pmod{8}

📌 Mod 125:** Solve \( n^3 \equiv 1 \pmod{125} \)

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Set equal to $ 2t + 1 $:
2at + (a + b) = 2t + 1.
2a = 2 \Rightarrow a = 1, \quad a + b = 1 \Rightarrow 1 + b = 1 \Right...
Thus, $ E(t) = t^2 $.
Then $ E(10) = 10^2 = 100 $.
Alternatively, recognize the recurrence as the discrete analog of deri...
E(1) = E(0) + 1 = 1, \quad E(2) = 1 + (2\cdot1 + 1) = 1 + 3 = 4, \quad...
So $ E(n) = \sum_{k=0}^{n-1} (2k + 1) = n^2 $, since sum of first $ n...
Hence, $ E(10) = 10^2 = 100 $.
Question: An oceanographer models the depth $ d(t) $ (in meters) of a...

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