CS70 Discrete Mathematics for Computer Science, Spring 2012
Homework 4
Out: 9 Feb. Due: 5pm, 16 Feb.
Instructions:
Start each problem on a new sheet. Write your name,
section number
and “CS70” on every sheet.
If you use more than one sheet for a problem, staple them together (but do
not
staple different problems together).
Put your solutions in the boxes on Soda level 2 by 5pm on Thursday: your solution to Q1 goes in box CS70–1, your
solution to Q2 goes in box CS70–2, and so on (
five
boxes total). You are encouraged to form small groups (two to four
people) to work through the homework, but you
must
write up all your solutions on your own.
1. [Practice with Modular Arithmetic]
(a) For each integer
x
mod 18, say whether or not
x
has an inverse, and if it does give the inverse.
(b) Use Euclid’s algorithm to compute
gcd(4725
,
273)
.
Show clearly the recursive calls made by the
algorithm.
(c) Use the extended gcd algorithm from class to compute the inverse of 7 mod 220. Show clearly the
recursive calls made by the algorithm and the results returned by each call.
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 Spring '08
 PAPADIMITROU
 Computer Science, Cryptography, Prime number, Euclidean algorithm

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