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We give asymptotic upper and lower bounds for the number of squarefree d (0 < d X) such that the equation x 2 dy 2 D 1 is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm 1 and give strong evidence in the direction of a conjecture due to P. Stevenhagen.
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Fouvry et al. (2010) studied this question.
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