Cryptography Reference
In-Depth Information
b.
42
x
+ 30
y
= 18
c.
252
x
+ 198
y
= 90
d.
11
x
+ 17
y
= 23
e.
12
x
+ 32
y
= 10
f.
12
x
+ 32
y
= 92
g.
36
x
+ 81
y
= 117
h.
252
x
+ 198
y
= 414
2.
Suppose for the apples and oranges example in this chapter that you have instead the
following amounts of money:
a.
2 dollars and 66 cents
b.
3 dollars
c.
7 dollars and 42 cents
d.
91 cents
Find all feasible solutions to the number of apples and oranges you should buy to exactly
exhaust your money.
3.
Dr. Fonebone goes to the post office to buy some 32¢ stamps and some 5¢ stamps. If
the doctor spent $3.45, how many stamps of each type could he have bought?
4.
Alien Commander Freenbean returns to her planet after a trip to Southeast Asia. If she
exchanges her foreign currency and receives a total of 941 gznardls, where she receives
37 gznardls for each Philippine peso and 63 gznardls for each Thai baht, how much of
each type of currency did she exchange? Are there multiple answers?
5.
You are at a classy restaurant with only $18.17 in your pocket, and you are starving.
Everything on the menu costs more than $20, except the following two items: bread-
sticks at $1.89 each, and large mountain oysters at $2.50 each. How much of each item
should you buy to spend all your money?
6.
What combination(s) of quarters and dimes totals $2.95?
7.
Write a GUI or an applet to enter the values of
a
,
b
, and
c
for the linear diophantine equa-
tion
ax
+
by
=
c
. Display a particular solution
x
=
x
0
,
y
=
y
0
in the window when the user
presses a “compute” button. Subsequent presses of the same button should produce an
alternate solution; the
n
th press should give the solution
x
=
x
0
+
bn
/
d
,
y
=
y
0
an
/
d
.
8.
Solve all of the following congruences for
x
, when solutions exist. If solutions do not
exist, explain why.
a.
6
x
4 (mod 14)
b.
9
x
7 (mod 15)
c.
9
x
21 (mod 24)
d.
21
x
9 (mod 24)
e.
35
x
21 (mod 56)
f.
8
x
7 (mod 15)
g.
348975893461
x
1 (mod 9238745892364)
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