ID 110912
Author
Content Type
Departmental Bulletin Paper
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.
Journal Title
Journal of Mathematics
ISSN
13467387
NCID
AA11595324
Volume
50
Start Page
43
End Page
47
Sort Key
43
Published Date
2016
EDB ID
FullText File
language
eng
TextVersion
Publisher
departments
Science and Technology