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On a problem in algebraic number theory

Name: On a problem in algebraic number theory
Creator: J. Wójcik
Keywords: 0301 basic medicine, 03 medical and health sciences, congruence, prime ideals, multiplicative group, 0101 mathematics, Schinzel's \(H\)-conjecture, 01 natural sciences, Algebraic numbers; rings of algebraic integers, Polynomials (irreducibility, etc.)

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1996 English Publisher:Cambridge University Press (CUP)Journal:Mathematical Proceedings of the Cambridge Philosophical Society, volume 119, pages 191-200 (issn: 0305-0041, eissn: 1469-8064,

Authors: J. Wójcik;

doi: 10.1017/s0305004100074090

On a problem in algebraic number theory

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Abstract

Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’

Keywords

congruence, prime ideals, multiplicative group, Schinzel's \(H\)-conjecture, Algebraic numbers; rings of algebraic integers, Polynomials (irreducibility, etc.)

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	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	4
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