Number theory, converting numbers too different bases

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SNOOTCHIEBOOCHEE
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Homework Statement



Show that for any fixed a and b, there is an algorithm to convert an n-digit number from
base a to base b with O(n^2) operations.

The Attempt at a Solution



Really i am completley lost here. Working backwards, i know to convert from base a to a base b you must use the division algorithm, which requires something on the order of (n^2) operations, but i really don't know how to show any of this.
 
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Any thoughts?