1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anarel [89]
3 years ago
5

Let ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication. Which of the followin

g are generators of ℤ×17? I.5 II.8 III.16
(I) 5.
(II) 8.
(III) 16.

(A) None.
(B) I only.
(C) II only.
(D) III only.
(E) I, II, and III
Mathematics
1 answer:
joja [24]3 years ago
7 0

Answer:  The correct option is (E) I, II and III.

Step-by-step explanation:  Given that ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication.

We are to select the correct generators of ℤ×17.

According to the given information, we can write

ℤ17 = {0, 1, 2, 3, . . . , 16}

and

ℤ×17 = {1, 2 , 3 , . . . 16}.

The generators of ℤ×17 are those elements which are co prime to 17.

Since all the elements from 1 to 16 are co prime to 17, so all the elements of the set  ℤ×17 are its generators.

Therefore, 5, 8 and 16, all are generators. So, i, ii and iii are generators.

Thus, (E) is the correct option.

You might be interested in
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
NeX [460]
Vertex at the origin and opening down → y=ax^2
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4

y=ax^2→y=-(1/4)x^2

7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4

Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m

Please, see the attached file.

Answer: Third option 15.75 m

3 0
3 years ago
Read 2 more answers
Solve for x: 5x + 15 = 75
yuradex [85]

Answer:

x = 12

Step-by-step explanation:

5x + 15 = 75

      -15   -15

5x = 60

x = 12

3 0
2 years ago
1/4 _ 1/5 is it < = >
Gre4nikov [31]

Answer:

1/4 > 1/5

Step-by-step explanation:

think of a candy bar. if you split it into 4 parts the prices would be bigger than if u had to break it into 5 parts. also remember that the smaller number eats the bigger number so the sign would be towards the 1/4

4 0
3 years ago
If $5,000 is borrowed with an interest of 12.3% compounded semi-annually, what is the total amount of money needed to pay it bac
jarptica [38.1K]

Answer:

$7153.03

Step-by-step explanation:

To find the total amount after 3 years, we can use the formula for compound tax:

P = Po * (1+r/n)^(t*n)

where P is the final value, Po is the inicial value, r is the rate, t is the amount of time and n depends on how the tax is compounded (in this case, it is semi-annually, so n = 2)

For our problem, we have that Po = 5000, r = 12.3% = 0.123, t = 3 years and n = 2, then we can calculate P:

P = 5000 * (1 + 0.123/2)^(3*2)

P = 5000 * (1 + 0.0615)^6

P = $7153.029

Rounding to the nearest cent, we have P = $7153.03

3 0
2 years ago
Find the sum and express it in simplest form <br> (6y-2c+2)+(-3y+4c)
Taya2010 [7]
Well, kid all you have to do is add like terms and place the subjected terms in alphabetical order. 
1. (6y-2c+2)+(-3y+4c)
2. 6y + - 3y = 3y
3. -2c+4c =2c
4. the positive in the first set of parenthesis has to term other than its number by itself. (so it remains alone and only positive 2)
5. take all the separate term answers and add them into a complete expression- 3y + 2c + 2: and that is all
3 0
3 years ago
Other questions:
  • 15 out of 25 students are boys in class. What percent are boys and what is the ratio in class?
    15·1 answer
  • A length of rope is stretched between the top edge of a building and a stake in the ground. The rope also touches a tree halfway
    6·1 answer
  • How do you make x the subject of:<br> 9x + 2 = 6x + 2y.
    11·1 answer
  • A group of students recycled 7 2/3 pounds of glass and 9 3/4 pounds of paper. How many pounds of glass and paper did the student
    12·2 answers
  • Help me with the question A and B please urgent...
    9·2 answers
  • Select the graph that represents the inequality <br><br> 2x + 3y &lt;= 6
    9·2 answers
  • What is the measure of the supplement of 82 degrees​
    12·1 answer
  • Read each problem carefully and solve as required then answer the questions that follow
    9·1 answer
  • Suppose line g is the line with equation y=x. Given A(9,-5), B(6,3), and C(-1,-6), what are the coordinates of the vertices of A
    10·1 answer
  • Which equation is linear function?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!