Cryptography Reference
In-Depth Information
17.
A satellite orbits the earth with period
is an integer. If
the satellite is directly overhead at 1300 (on a 24-hour clock), then 7 orbits later is again
directly overhead at 1800, what is
p
hours, where 0 <
p
< 24, and
p
p
, the orbital period of the satellite?
18.
Old Faithless is a geyser in Tibet that erupts every 5 hours. If it erupted at exactly 12
noon on June 2, 2000, when did it next erupt at exactly 12 noon?
19.
The Screechids is a meteor shower through which the planet Mongo passes every 143
of its days. Mongo passed through the Screechids on its New Year's day in its year
10793. If the orbital period of Mongo is 299 of its days, when did Mongo next pass
through the Screechids on New Year's day? (Mongo has no leap years, nor any other
calendar adjustments.)
20.
Consider now how you may solve a system of linear diophantine equations, as in the
system
3
x
+ 3
y
+ 2
z
= 11
5
x
+
y
+ 3
z
= 10
which has as a particular solution
= 1. Explain how such a solution (or
any other particular solution) could be found. Does this system have infinitely many
solutions?
x
= 1,
y
= 2,
z
21.
Solve the following system of linear diophantine equations.
3
x
+
y
+ 7
z
= 14
4
x
+ 3
z
+
z
= 12
22.
Solve the following system of linear diophantine equations.
3
x
+
y
+ 7
z
= 14
4
x
+ 3
z
+
z
= 12
2
x
+ 5
z
+
z
= 10
23.
Solve the following system of linear diophantine equations.
3
x
+
y
+ 7
z
= 14
4
x
+ 3
z
+
z
= 12
2
x
+ 5
z
+
z
= 9
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