Titlebook: Binary Quadratic Forms; Classical Theory and Duncan A. Buell Book 1989 Springer-Verlag New York Inc. 1989 Arithmetic.Finite.algebra.calculu

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Miscellaneous Facts II,We shall consider in this chapter some basic topics, some of which are clearly interrelated.

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Factoring with Binary Quadratic Forms,In the opening paragraphs of Article 329 of the ., Gauss, a master at calculating, writes [pp. 396–397],

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Elementary Concepts,, ✱) or (., ✱, ✱) if the second or second and third coefficients are irrelevant or unknown or are easily computed by the discriminant formula. Note that Δ ≡ 1 or Δ ≡ 0 (mod 4) is necessary and that . ≡ Δ (mod 2). Generally assume also that we are dealing with . forms, for which gcd(., ., .) = 1.

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https://doi.org/10.1007/978-3-531-90181-7, ✱) or (., ✱, ✱) if the second or second and third coefficients are irrelevant or unknown or are easily computed by the discriminant formula. Note that Δ ≡ 1 or Δ ≡ 0 (mod 4) is necessary and that . ≡ Δ (mod 2). Generally assume also that we are dealing with . forms, for which gcd(., ., .) = 1.

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978-1-4612-8870-1Springer-Verlag New York Inc. 1989

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