Question
In: Advanced Math
Show that the numbers 1, 3, 3^2 , . . . , 3^15 and 0 for...
Show that the numbers 1, 3, 3^2 , . . . , 3^15 and 0 for a complete system of residues (mod 17). Do the numbers 1, 2, 2^2 , . . . , 2^15 and 0 constitute a complete system of residues (mod 17)?
Solutions
Expert Solution
Since 
is a cyclic group of order 
, the set 
is a complete set of residue modulo 
if and only if
has order .
Now, by Fermat's little theorem, we have 
. On the other hand, 
, which implies 
. Therefore, 
.
By Lagrange's theorem, the order of any element in
must divide the order of the group
itself. Thus, if
does not have order , its order will be one
of 
. In any
case, it must satisfy 
which is not the case. Hence,
has order .
As explained above, this shows that
is a complete system of residues modulo .
For the set 
, we notice that 
. Thus, 
has order 
. Therefore,
is not a complete system of residues modulo .
Colby Messinger answered 2 years agoRelated Solutions
Consider the set of integer numbers from 0 to 9, that is {0, 1, 2, 3,...
Consider the set of integer numbers from 0 to 9, that is {0, 1,
2, 3, 4, 5, 6, 7, 8, 9}. Bob wishes to use these numbers to create
a 7-digit password to secure his new laptop. Note that each number
can appear in any position (for example, 0 can be the first number
in the password). (a) Find the number of 7-digit passwords that are
possible. (b) Find the number of 7-digit passwords with distinct
digits. (c) Find...
DATA 3 8 2 15 2 2 0 0 4 5 2 7 0 1 5...
DATA
3
8
2
15
2
2
0
0
4
5
2
7
0
1
5
3
0
2
5
4
1
6
9
5
3
1
2
10
6
1
1
2
1
19
6
6
6
7
0
4
1
1
1
0
1
9
2
2
2
1
16
10
10
5
2
3
1
4
4
4
3
6
2
8
5
2
7
1
6
4
0
3
1
1
1
Background:
A group of...
exampleInput.txt 1 2 3 0 2 3 4 0 1 3 5 0 1 2 6...
exampleInput.txt
1 2 3
0 2 3 4
0 1 3 5
0 1 2 6
1 5 6 8
2 4 6 7
3 4 5 9 10
5 8 9
4 7 9
6 7 8
6
How can I detect when 'cin' starts reading from a new line. The
amount of numbers in each row is unknown. I need them in type 'int'
to use the data.
The Fibonacci sequence is the series of numbers 0, 1, 1, 2, 3, 5, 8,.... Formally,...
The Fibonacci sequence is the series of numbers 0, 1, 1,
2, 3, 5, 8,.... Formally, it can be expressed as:
fib0 = 0
fib1 = 1
fibn = fibn-1 + fibn-2
Write a multithreaded C++ program that generates the
Fibonacci series using the pthread library. This program should
work as follows: The user will enter on the command line the number
of Fibonacci numbers that the program will generate. The program
will then create a separate thread that will...
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)MEAN –
B.)MEDIAN -
C.)MODE -
D.)STANDARD DEVIATION –
E.)5 NUMBER SUMMARY –
F.)BOX AND WHISKERS PLOT –
G.) OUTLIERS-
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)5 NUMBER SUMMARY –
B.)BOX AND WHISKERS PLOT –
C.) OUTLIERS-
({s^3} + 6{s^2} + 15s + 15)=0 Solve for s - please show all work
({s^3} + 6{s^2} + 15s + 15)=0
Solve for s - please show all work
?" + 3?′ + 2? = ????, ?(0) = 0, ?′(0) = 2 1) Please solve...
?" + 3?′ + 2? = ????, ?(0) = 0, ?′(0) = 2
1) Please solve using an annihilator
2) Please solve using the Method of Variation of Parameters
Thank you.
A= 1 2 4 0 1 -2 -1 0 1 2 0 3 8 1 4...
A=
1
2
4
0
1
-2
-1
0
1
2
0
3
8
1
4
. Let W denote the row space for A.
(a) Find an orthonormal basis for W and for W⊥.
(b) Compute projW⊥(1 1 1 1 1 ).
Production costs Worker-hours (Input) Widgets (Output) 0 0 1 3 2 8 3 15 4 20...
Production costs
Worker-hours (Input) Widgets (Output)
0 0
1 3
2 8
3 15
4 20
5 24
6 27
7 29
8 30
9 30
10 29
Fixed cost = $120
Variable cost = $15
a) Given the above widget production function information, graph
the total product curve, clearly labeling everything.
b) Given the cost information above, graph the total cost curve.
Add columns to the table as needed.
c) Describe the pattern of marginal returns and marginal costs....
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