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<br>Nonetheless, it may be approximated arbitrarily carefully by such rational numbers. These two approximations are the respective elementary options of each Pell's equation, to which further options are algebraically related. Newton's methodology for locating the root of an arbitrary function. For a typical guess, the approximation converges quadratically (roughly doubles the variety of appropriate digits at every step). 1 − φ . − φ ¯ n 5 . 1

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