Cryptography Reference
In-Depth Information
h.
46873258738754865
x
3 (mod 9283765872587542121751)
9.
Find an inverse of
a.
10 modulo 21
b.
5 modulo 8
c.
6 modulo 21
d.
13 modulo 30
e.
13 modulo 143
f.
14 modulo 15
g.
33 modulo 121
h.
985 modulo 2527
i.
8 modulo 27
j.
9 modulo 14
when such an inverse exists. If it does not exist, state the reason.
10.
Prove proposition 18.
11.
Prove proposition 19.
12.
Prove proposition 20.
13.
Consider how you might solve linear diophantine equations in more than two variables;
for example, the equation
3
x
+ 2
y
+ 5
z
= 26
has
x
= 5,
y
= 3,
z
= 1 as a particular solution. How might you find this particular solu-
tion? Or any other? One approach you might take is to solve the equation
3
x
+ 2
y
+ 5
z
= 1
where (3, 2, 5) = 1, and remember that (3, 2, 5) = ((3, 2), 5). That is, you can solve
3
x
+ 2
y
= (3, 2) = 1
then use these values for
x
and
y
to solve the equation in three variables using the proper
substitutions.
14.
What combination(s) of quarters, dimes, and nickels equals 85ยข?
15.
How many ways can change be made for a dollar using
a.
quarters and dimes?
b.
quarters, dimes, and nickels?
16.
What time does a 12-hour clock read
a.
35 hours after 8 o'clock?
b.
73 hours after 5 o'clock?
c.
58 hours before 1 o'clock?
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