ID | 110912 |
Author | |
Content Type |
Departmental Bulletin Paper
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Description | In 1922 R. D. Carmichael conjectured that for any natural number n there exist infinitely many natural numbers m such that φ(n) = φ(m). It is well known that this conjecture can be proved under the assumption of the famous unproved hypothesis of Schinzel and Sierpiński. In this short note, we shall show the Hypothesis of Schinzel and Sierpiński implies more precisely that the existence of infinitely many cyclotomic fields Q(ζn) and Q(ζm) with isomorphic absolute Galois groups. Here ζn and ζm are primitive nth and mth roots of unity with m ≠ n.
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Journal Title |
Journal of Mathematics
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ISSN | 13467387
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NCID | AA11595324
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Volume | 50
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Start Page | 43
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End Page | 47
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Sort Key | 43
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Published Date | 2016
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EDB ID | |
FullText File | |
language |
eng
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TextVersion |
Publisher
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departments |
Science and Technology
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