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MATH 135
Fall 2006
Final Examination
Wednesday 20 December 2006, 12:30 p.m. to 3:00 p.m.
1. In each part of this problem, full marks will be given if the correct answer is written in the box.
If your answer is incorrect, your work will be assessed for part marks.
(a) Convert

√
15 +
√
5
i
to polar form.
[3]
(b) Write
5 + 15
i
2

i
+ 2
i
in standard form.
[3]
(c) Determine an integer
a
∈
Z
with 0
≤
a <
23 and [
a
] = [7]

1
·
[3] + [11] in
Z
23
.
[3]
2. Determine the complete solution to the linear congruence 532
x
≡
147 (mod 637).
[7]
3. Determine the complete solution to the congruence
x
31
+ 17
x
≡
43 (mod 55).
[10]
4. (a) Ron wants to send a message to Hermione after encrypting it using RSA.
[7]
Hermione’s public key is (
e, n
) = (11
,
221) and her private key is (
d, n
) = (35
,
221).
Using the appropriate key, encrypt the message
M
= 137 that Ron wants to send to
Hermione.
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This note was uploaded on 10/21/2010 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.
 Fall '08
 ANDREWCHILDS
 Math

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