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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You don't need induction.
we have a contradiction.
can you explain why its a contradiction
Originally Posted by ilovepurerubbish can you explain why its a contradiction It contradicts the choice of . Do you see that we could as well take instead of (which contradicts the fact that we always take maximal possible 's)?
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