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component form of a vector - GetMeFoodie

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 $ 10 \cdot 3281 = 32810 $, $ 6 \cdot 3281 = 19686 $, total $ 32810 + 19686 = 52496 $?

📌 But $ 52496 $, $ 52500 - 52496 = 4 $? So remainder is 4?

📌 But earlier modular computation gave 12. Contradiction.

📌 Recheck: $ 5000 \mod 16 $:

📌 $ 16 \cdot 312 = 5016 $, too big.

📌 Try: $ 10^3 = 1000 $, $ 1000 \mod 16 $:

📌 $ 16 \cdot 62 = 992 $, $ 1000 - 992 = 8 $, so $ 1000 \equiv 8 \pmod{16} $

📌 Then $ 1000 \equiv 8 $, so $ 5000 = 5 \cdot 1000 \equiv 5 \cdot 8 = 40 \equiv 8 \pmod{16} $ ($ 40 - 2 \cdot 16 = 8 $)

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