Cryptography Reference
In-Depth Information
2.
Solve the previous systems of linear congruences without using the Chinese Remain-
der Theorem.
3.
Willie the woodchuck is building a dam for his family. After gnawing down trees all
day he stacks the logs in the mud in rows of 5, and notices he has 1 left over. Disgrun-
tled, he stacks them in rows of 6 and notices he has 2 logs remaining. Highly upset
now, Willie chews one of the logs to bits in a fit of rage (so he has 1 less log now), then
stacks the logs in rows of 7 and has none remaining. What is the minimum number of
logs Willie produced that day?
4.
Francine the dancing gorilla is dividing up coconuts for her family. If she divides them
up equally among all her 46 children, she has 3 coconuts left over, but if she divides
them up only among her 25 favorite children, she has 2 coconuts remaining. What is
the minimum number of coconuts Francine has?
5.
Redneck Slim is planting petunias for his sweetheart Daisy Mae. If he places them in
9 rows, he has 2 plants left over. If he puts them in 10 rows, he has 3 plants left over,
but if he puts them in 11 rows he has exactly 1 plant left over for his date Saturday
night. What is the minimum number of petunia plants?
6.
Show that the system of congruences
x
a
1
(mod
m
1
)
x
a
2
(mod
m
2
)
x
a
n
(mod
m
n
)
has a solution iff the gcd of
. This can serve
as a check for systems which do not have moduli that are pairwise relatively prime.
m
i
and
m
k
divides
a
i
a
k
where 1
≤
i
<
k
≤
n
7.
Solve the following systems of linear congruences:
a.
x
7 (mod 24)
x
23 (mod 56)
b.
x
80 (mod 95)
x
4 (mod 38)
x
50 (mod 60)
8.
Write a static solveMultipleModuli() method in the BigIntegerMath class to find a par-
ticular solution to linear systems of congruences with multiple moduli that need not be
pairwise relatively prime. (Thus, you cannot use the Chinese Remainder Theorem.)
Search WWH ::
Custom Search