We extend our previous results concerning the equation a2 + bc = n to all primes n and deal also with the general case of non-square n. Moreover, we provide partial results on patterns of ‘1’ and ‘11’ in the continued fractions of √n.
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An upper estimate is given for the least prime q such that (d/q) = 1 and (p/q) = −1, where d ǂ 0 is a given integer and p is a given prime satisfying p ≡ 1 (mod 8) and (d/p) = 1.
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