Titlebook: Computational Algebra and Number Theory; Wieb Bosma,Alf Poorten Book 1995 Springer Science+Business Media Dordrecht 1995 Category theory.G

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Sorin Adam Matei,Brian C. Britt, where .. (≠1) is even, such that ..(.., .) ∈ ... for all . ≥ 0..The classical generalisation of the Kummer congruence is . It will be shown that this is periodic in the sense that ..(.., .) ≡ ..(.., .) mod ... if . ≡ . mod (. ? 1) with . > 0 and . ≡ . mod (. ? 1).

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Short Representation of Quadratic Integers,ynomial time compute norms, signs, products, and inverses of numbers in . and principal ideals generated by numbers in .. We also show how to compare numbers given in compact representation in polynomial time.

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https://doi.org/10.1007/978-1-349-12448-0 states the results for the case . ≡ 1 mod 4, and gives some numerical examples. The proofs, generalisations to other square-free ., and similar results for the identities of Gauss and Dirichlet, appear elsewhere[1].

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https://doi.org/10.1007/978-1-349-12448-0e also to .-based approaches to more general quantifier elimination problems. We present a version of the . algorithm which solves the consistency problem for conjunctions of strict inequalities, and which runs faster than the original method applied to this problem.