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Compact representation of quadratic integers and integer points on some elliptic curves

Compact representations are used to store the fundamental unit of the quadratic order O_K. The reason for doing this is that there is an infinite set of quadratic orders, such that the binary length of the fundamental unit is exponential in log d. This makes it impossible to create an algorithm for solving the Pell equation with complexity less than exponential. Compact representations are polynomial in log d, and allow faster algorithms for solving the Pell equation.

Pellian equations ; elliptic curves

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