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Home » \( n = 7 \): \( 343 \equiv 7 \mod 8 \) - Veritas Home Health

\( n = 7 \): \( 343 \equiv 7 \mod 8 \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Actually: 2⁸⁰ = 120892581961462417476233206292340255376

📌 2⁶⁴ = 18446744073709551616

📌 Difference = 120892581961462417476233206292340255376 − 18446744073709551616 = 120892059414852865724713604639740173760

📌 But for compact:

📌 ≈ 1.2089 × 10¹⁹ → but per format, use exact expression? But answer expected number.

📌 #### 120892059414852865724713604639740173760

📌 But this is too long. Instead, recognize:

📌 Factor: 2⁶⁴(2¹⁶ − 1) = 18446744073709551616 × (65536 − 1) = 18446744073709551616 × 65535

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Solution: Let $ a $ = units of A, $ b $ = units of B.
$$ a + b = 15 $$
$$ 12a + 8b = 156 $$
From the first equation, $ b = 15 - a $. Substitute into the second:
$$ 12a + 8(15 - a) = 156 $$
$$ 12a + 120 - 8a = 156 $$
$$ 4a = 36 $$
$$ a = 9 $$
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