Math 4330, Homework 5, 2/19/2014 : Due 2/24/2014
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1. Show that if u > v then (u mod v) ≤ u/2.
2. Use the previous result to prove that in Algorithm A, Step A2 is executed no more
than 1 + 2 log2 u times. (In particular, it follows that the Euclidean Algorithm is
polynomial-time in the input size which is log2 u + log2 v.)
3. Implement Algorithm X verbatim (i.e., name your variables the same way and use
comments to label the steps X1, X2, and X3). Use it to find an integer x such that
171x ≡ 1 (mod 10000000000001) .
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Chris Monico, and may not be reproduced in any form without
written permission from the author.
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