I should do the searching... but just in case. Is it true that one can get the coefficients of less degree than the starting elements if one is in an Euclidean Domain? In the case of integers this amounts to saying that

there are x,y ∈ Z wiht |x|<max(a,b), |y|<max(a,b) with xa+yb=gcd(a,b)

Just in case. I'll try to find out though :) Pfortuny 09:26, 20 Apr 2004 (UTC)

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