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標(biāo)題: Titlebook: Number Theory for Beginners; André Weil Textbook 1979 Springer-Verlag New York Inc. 1979 Zahlentheorie.algebra.form.mathematics.number the [打印本頁]

作者: 誤解    時(shí)間: 2025-3-21 20:05
書目名稱Number Theory for Beginners影響因子(影響力)




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https://doi.org/10.1007/978-1-4612-9957-8Zahlentheorie; algebra; form; mathematics; number theory; production; time; university; vi
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作者: 手工藝品    時(shí)間: 2025-3-22 05:04
,§ XI,vial, we assume .≠0. If then, in the field ., . is a solution of x.=a, an element . of . is also a solution if and only if ...1. Therefore, if x.=a has a solution in ., it has as many solutions as . contains .. roots of unity, i.e. roots of ...1.
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,§ III,Integers .,. are called mutually relatively prime if their g.c.d. is 1.
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,§ IV,An integer .>1 is called a prime if it has no other positive divisor than itself and 1.
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,§ V,A commutative (or “abelian”) group is a set ., together with a binary operation between elements of ., satisfying the following axioms (in which the group operation is denoted by +):
作者: anniversary    時(shí)間: 2025-3-23 01:26
,§ VI,If . is any integer >0, we define the multiplication of congruence classes by putting .; in fact, property (E), § V, shows that the right-hand side depends only upon the two classes in the left-hand side and not upon the choice of their representatives ..
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,§ VIII,Theorem II.1 shows that every subgroup . of . is either 0 or generated by its smallest element .0. in the latter case it is generated by . or also by —., but by no other element of . For cyclic groups, we have:
作者: falsehood    時(shí)間: 2025-3-23 16:22
,§ IX,In order to consider polynomials with coefficients in a field ., and equations over such fields, we begin by reviewing some elementary properties of polynomials over an arbitrary field .; these are independent of the nature of that field, and quite analogous to the properties of integers described above in §§ II, III, IV.
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,§ X,Let G be a group of order m. If, for every divisor d of m, there are no more than d elements of G satisfying x.=1, G is cyclic.
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Textbook 1979t the problem sessions so on became desultory. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. Rather than a literal reproduction of the course, they should be regarded as its skeleton; they were supplemented by references to stan- dard text-books on alge
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,§ XI,vial, we assume .≠0. If then, in the field ., . is a solution of x.=a, an element . of . is also a solution if and only if ...1. Therefore, if x.=a has a solution in ., it has as many solutions as . contains .. roots of unity, i.e. roots of ...1.
作者: 變異    時(shí)間: 2025-3-25 00:19
,§ XII,onsisting of the classes (±1 mod . we apply to . and . the definitions and lemma of § VIII. If . is an element of ., it belongs to one and only one coset . this consists of the two elements (±. mod . there are . such cosets, viz., the cosets (±1 mod .), (±2 mod .),...(±. mod .). If, in each coset, w
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作者: Matrimony    時(shí)間: 2025-3-25 07:39
André Weile, verletzungsbezogene Patientenhinweise.Mit Themenkomplex ".Dieses Lexikon enth?lt alles, was ein Therapeut und Arzt über die Behandlung von Verletzungen des Bewegungsapparats wissen muss. Für die Neuauflage wurde der gesamte Inhalt überarbeitet und durch weitere typische Sportlerverletzungen, insb
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,§ XII,every integer prime to . is congruent to one and only one of the integers .... modulo .. For the purposes of the next lemma, which is due to Gauss and known as Gauss’ lemma, such a set ...} will be called a “Gaussian set” modulo .. The simplest such set is {1,2,...,.}.
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