Cryptography Reference
In-Depth Information
E
XAMPLES
.
• lcm(36, 78) = 36 · 78/(36, 78) = 36 · 78/6 = 6 · 78 = 468
• lcm(21, 56) = 21 · 56/(21, 56) = 21 · 56/7 = 3 · 56 = 168
• lcm(100, 2050) = 100 · 2050/(100, 2050) = 100 · 2050/50 = 2 · 2050 = 4100
EXERCISES
1.
Show that
a.
5|20
b.
7|42
c.
8|8
d.
1|55
e.
7|0
f.
342|0
2.
Give the divisors of
a.
72
b.
37
c.
30
d.
27
e.
0
3.
Using the division algorithm, find integers
q
and
r
for the following equations. Remem-
ber, 0
≤
r
<
b
.
a.
47 = 5
q
+
r
b.
153 = 7
q
+
r
c.
143 = 8
q
+
r
d.
7 = 9
q
+
r
e.
0 = 32
q
+
r
f.
1 = 6
q
+
r
r
4.
Prove proposition 2.
5.
Determine which, if any, of the following integers are primes. For any that are not
prime, list the positive factors.
a.
g.
6 = 6
q
+
77
b.
78
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