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Zbl 1011.11003
Glasby, S.P.
Extended Euclid's algorithm via backward recurrence relations. (English)
[J] Math. Mag. 72, No.3, 228-230 (1999). ISSN 0025-570X

After using Euclid's algorithm to find $(a,b)$ one can either work forward from the pair $a,b$ or backwards from the pair $(a,b),0$ to find $x,y$ such that $ax+by= (a,b)$. The author claims that working backwards is better for calculation by hand, and also pedagogically, but that working forwards is better for use with a computer.
[H.J.Godwin (Egham)]

MSC 2000:: *11A05 Multiplicative structure of the integers

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