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Home » 8192 → 4096 (2) - Dachbleche24

8192 → 4096 (2) - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $$ (16a + 4b + c) - (4a + 2b + c) = 360 - 120 \Rightarrow 12a + 2b = 240 \Rightarrow 6a + b = 120 \quad \text{(i)} $$

📌 Subtracting equation (2) from (3):

📌 $$ (36a + 6b + c) - (16a + 4b + c) = 720 - 360 \Rightarrow 20a + 2b = 360 \Rightarrow 10a + b = 180 \quad \text{(ii)} $$

📌 Subtracting (i) from (ii):

📌 $$ (10a + b) - (6a + b) = 180 - 120 \Rightarrow 4a = 60 \Rightarrow a = 15 $$

📌 Substitute $ a = 15 $ into (i):

📌 $$ 6(15) + b = 120 \Rightarrow 90 + b = 120 \Rightarrow b = 30 $$

📌 Substitute $ a = 15 $, $ b = 30 $ into (1):

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$ k = 1 $: $ (-1)^1 inom{4}{1} \cdot 3^6 = -1 \cdot 4 \cdot 729 = -29...
$ k = 2 $: $ (-1)^2 inom{4}{2} \cdot 2^6 = 1 \cdot 6 \cdot 64 = 384 $
$ k = 3 $: $ (-1)^3 inom{4}{3} \cdot 1^6 = -1 \cdot 4 \cdot 1 = -4 $
$ k = 4 $: $ (-1)^4 inom{4}{4} \cdot 0^6 = 1 \cdot 1 \cdot 0 = 0 $
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oxed{1560}
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