For $x,y \in \mathbf{N}$ the equation: $$x^2 - 11 y^2 = 1.$$ has infinite many solutions. Find three solutions other than $(10,3)$.
Hint: Use continued fractions.
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
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