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Home » \binom31 \times \binom73 - ToelettAPP

\binom31 \times \binom73 - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \sqrt{x^2 + y^2 + z^2} = 1 \quad \Rightarrow \quad x^2 + y^2 + z^2 = 1

📌 The distance from \((1, 0, 0)\) to \((x, y, z)\) is:

📌 \sqrt{(x-1)^2 + y^2 + z^2} = 1 \quad \Rightarrow \quad (x-1)^2 + y^2 + z^2 = 1

📌 x^2 - 2x + 1 + y^2 + z^2 = 1 \quad \Rightarrow \quad x^2 + y^2 + z^2 - 2x + 1 = 1

📌 Since \(x^2 + y^2 + z^2 = 1\), we have:

📌 - 2x + 1 = 1 \quad \Rightarrow \quad 2 - 2x = 1 \quad \Rightarrow \quad x = \frac{1}{2}

📌 Since \(x\) must be an integer, this is not possible. Re-evaluate using symmetry and integer constraints. Consider \((x, y, z) = \left(\frac{1}{2}, \frac{1}{2}, \frac{\sqrt{2}}{2}\right)\) is known for symmetry, but integers require:

📌 Try \((\frac{1}{2}, \frac{1}{2}, \frac{\sqrt{2}}{2})\) scaled to integers, \( (1, 1, 1) \) by symmetry and integer requirement.

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