Primes, permutations and primitive roots.

Lewittes, Joseph; Kolyvagin, Victor

Displaying similar documents to “Primes, permutations and primitive roots.”

Square Lehmer numbers

Wayne McDaniel (1993)

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Modular forms and class number congruences

Antone Costa (1992)

Acta Arithmetica

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On integers not of the form n - φ (n)

J. Browkin, A. Schinzel (1995)

Colloquium Mathematicae

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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).

On $D$ sot hat $x^{2} - D y^{2}$ represents $m$ and $- m$ and not $- 1$ .

Robertson, John P. (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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The diophantine equation x² + 19 = yⁿ

J. H. E. Cohn (1992)

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Quasi-identities of congruence-distributive quasivarieties of algebras.

Nurakunov, A.M. (2001)

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Weyl almost periodic selections of supports of measure-valued functions.

Danilov, L.I. (2006)

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Simple proofs of some generalizations of the Wilson’s theorem

Jan Górowski, Adam Łomnicki (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.

Modified proof of a local analogue of the Grothendieck conjecture

Victor Abrashkin (2010)

Journal de Théorie des Nombres de Bordeaux

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A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p \neq 0$ and the category of absolute Galois groups of fields $K$ together with their ramification filtrations. The case of characteristic 0 fields $K$ was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case $p > 2$ (but with no restrictions on the characteristic of $K$ )....

Lagrange’s Four-Square Theorem

Yasushige Watase (2014)

Formalized Mathematics

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This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.