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Home » n^3 \equiv 1 \pmod1000. - Tacotoon

n^3 \equiv 1 \pmod1000. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\frac{a + \frac{1}{2} \cdot \frac{2a\sqrt{7}}{3}}{a - \frac{3}{2} \cdo...
Multiply numerator and denominator by $ 1 + \sqrt{7} $:
\frac{(3 + \sqrt{7})(1 + \sqrt{7})}{3(1 - 7)} = \frac{3(1) + 3\sqrt{7}...
But since the progression is real and the context suggests positive te...
Let $ r = \frac{a + \frac{d}{2}}{a - \frac{3d}{2}} $. Let $ x = \frac{...
r = \frac{1 + \frac{x}{2}}{1 - \frac{3x}{2}}.
Substitute $ x = \sqrt{\frac{28}{9}} = \frac{2\sqrt{7}}{3} $:
r = \frac{1 + \frac{1}{2} \cdot \frac{2\sqrt{7}}{3}}{1 - \frac{3}{2} \...
As before, this evaluates to $ -\frac{5 + 2\sqrt{7}}{9} $, but this is...
Alternatively, let the first term be $ A $, common difference $ d $, s...

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