On a problem of Bednarek
Florian Luca (2012)
Communications in Mathematics
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We answer a question of Bednarek proposed at the 9th Polish, Slovak and Czech conference in Number Theory.
Florian Luca (2012)
Communications in Mathematics
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We answer a question of Bednarek proposed at the 9th Polish, Slovak and Czech conference in Number Theory.
Danilov, L.I. (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Wayne McDaniel (1993)
Colloquium Mathematicae
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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 (k = 1, 2,...) is of the form n - φ(n).
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.
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 with finite residue fields of characteristic and the category of absolute Galois groups of fields together with their ramification filtrations. The case of characteristic 0 fields was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case (but with no restrictions on the characteristic of )....
Antone Costa (1992)
Acta Arithmetica
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Robertson, John P. (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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