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Home » 2k \equiv 6 \pmod11 - Dachbleche24

2k \equiv 6 \pmod11 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 But better to use algebra:

📌 |a - b|^2 = (a - b)^2 \quad ext{if real, but not necessarily.}

📌 |a - b|^2 = (a - b)(\overline{a} - \overline{b}) = |a|^2 + |b|^2 - a\overline{b} - \overline{a}b

📌 Not helpful unless complex conjugates known.

📌 Alternate: treat \( a \) and \( b \) as roots of quadratic:

📌 x^2 - (a + b)x + ab = 0 \Rightarrow x^2 - 4x + 3 = 0

📌 Roots: \( x = rac{4 \pm \sqrt{16 - 12}}{2} = rac{4 \pm 2}{2} = 3, 1 \)

📌 So \( a, b = 1, 3 \) (up to order), both real.

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