𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a paper by J. Rosen

✍ Scribed by L. Abellanas; A. Galindo; Alonso L. Martinez


Book ID
104758393
Publisher
Springer
Year
1979
Tongue
English
Weight
25 KB
Volume
3
Category
Article
ISSN
0377-9017

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✦ Synopsis


In a recent paper [1 ], J. Rosen claims to have generalized a result given in [2], characterizing Ker 6/6u. Surprisingly enough the author does not refer to another paper [3] quoted in [2] and published in the same issue of this journal in which the equality Ker 6/6u = Ran D ( 1 ) was already rigorously established in full generality. On the other hand, the essential step in the proof of necessity in [ 1 ], namely Ker 6/6u C Ran D (2) is, in our opinion, lacking. When one goes into the details of this step, one is compelled to an argument such as that used in [3].


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Let c E IN. For d E Z with gcd (d, c) = 1 let 6(d, c) be defined by d . 6 ( d , c) I 1 mod c, 1 5 6(d, c) 5 c. Let s, t E IN with 1 5 s 5 c, 1 5 t 5 c. The main result is that for arbitrary fixed E > 0, but uniformly over c, s and t, # { d E I N : ( ~, d ) = l , I 5 d S S and 1 < 6 ( d , c ) < t } =