18. Prove that in a Euclidean ring R, (a, b) can be found as follows : b= 90 a+ r,, where d (r)
18. Prove that in a Euclidean ring R, (a, b) can be found as follows : b= 90 a+ r,, where d (r)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:18. Prove that in a Euclidean ring R, (a, b) can be found
as follows :
63D90 a+ r¡, where d (r) <d (a)
aj = q¡rj+r2, where d (r2) < d (r)
= 92r2+ r3, Wwhere d (r3) < d (r2)
%3D
and
rn= (a, b).
%3D
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