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\equiv 3 \pmod6 - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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\Rightarrow (x^2 + y^2 + z^2) - 2x - 2y + 2 = 2
\Rightarrow 2 - 2x - 2y + 2 = 2 \Rightarrow -2x - 2y = -2 \Rightarrow...
Distance from $(1,0,1)$:
\Rightarrow x^2 - 2x + 1 + y^2 + z^2 - 2z + 1 = 2
\Rightarrow (x^2 + y^2 + z^2) - 2x - 2z + 2 = 2
\Rightarrow 2 - 2x - 2z + 2 = 2 \Rightarrow -2x - 2z = -2 \Rightarrow...
From (2) and (3), we have:
x + y = 1, \quad x + z = 1 \Rightarrow y = z
From the first equation:
x^2 + y^2 + z^2 = 2 \Rightarrow x^2 + 2y^2 = 2

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