Let be the successive remainders in the Euclidean Algorithm applied to and . Show that for all .

I'm thinking that this is proven by induction but I am stuck on the inductive step.

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- Sep 2nd 2009, 12:34 AMordinalhighEuclid's algorithm question
Let be the successive remainders in the Euclidean Algorithm applied to and . Show that for all .

I'm thinking that this is proven by induction but I am stuck on the inductive step. - Sep 2nd 2009, 01:21 AMTaluivren
You don't need induction.

Suppose that

we have

a contradiction. - Sep 2nd 2009, 09:47 AMilovepurerubbish
can you explain why its a contradiction

- Sep 2nd 2009, 10:02 AMTaluivren