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Home » \mathbfv imes \mathbfa = a(-4) - b(3) = -4a - 3b - Dachbleche24

\mathbfv imes \mathbfa = a(-4) - b(3) = -4a - 3b - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 So the minute number of the 100th signal is $ \boxed{1287} $.

📌 Question: What is the remainder when $ 123456789 $ is divided by 9?

📌 Solution: Use the divisibility rule for 9: the remainder when a number is divided by 9 is the same as the remainder when the sum of its digits is divided by 9.

📌 Sum of digits of 123456789:

📌 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

📌 Now compute $ 45 \mod 9 $:

📌 Question: What is the greatest common divisor of $ 12345 $ and $ 98765 $?

📌 Solution: Use the Euclidean algorithm:

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Number of non-negative integer solutions: $ \binom{3 + 4 - 1}{3} = \bi...
So there are 20 valid configurations (binary strings) with exactly 3 n...
For each such configuration, the probability is:
\left(\frac{1}{3}\right)^3 \left(\frac{2}{3}\right)^5 = \frac{1^3 \cdo...
Since each configuration has the same probability and they are mutuall...
Total probability:
\cdot \frac{32}{6561} = \frac{640}{6561}
Thus, the probability is:
\boxed{\frac{640}{6561}}
$$Question: What is the greatest common divisor of $ 5^m - 1 $ and $ 5...

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