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
Phoenix [80]
3 years ago
7

For each x and n, find the multiplicative inverse mod n of x. Your answer should be an integer s in the range 0 through n - 1. C

heck your solution by verifying that sx mod n = 1.(a) x = 52, n = 77(b) x = 77, n = 52(c) x = 53, n = 71(d) x = 71, n = 53
Mathematics
1 answer:
krok68 [10]3 years ago
6 0

Use the Euclidean algorithm to express 1 as a linear combination of x and n.

a. 52^{-1}\equiv40\pmod{77} because

77 = 1*52 + 25

52 = 2*25 + 2

25 = 12*2 + 1

so we can write

1 = 25 - 12*2 = 25*25 - 12*52 = (77 - 52)(77 - 52) - 12*52 = 77^2 - 2*52*77 + 52^2 - 12*52

Taken modulo 77 leaves us with

1\equiv52\cdot52-12\cdot52\equiv40\cdot52\pmod{77}\implies52^{-1}\equiv40\pmod{77}

b. First, 77\equiv25\pmod{52}, so really we're looking for the inverse of 25 mod 52. We've basically done the work in part (a) already:

1 = 25*25 - 12*52

Taken modulo 52, we're left with

1\equiv25\cdot25\pmod{52}\implies25^{-1}\equiv25\pmod{52}

c. The EA gives

71 = 1*53 + 18

53 = 2*18 + 17

18 = 1*17 + 1

so we get

1 = 18 - 17 = 3*18 - 53 = 3*71 - 4*53

so that taken module 71, we find

1\equiv(-4)\cdot53\pmod{71}\implies53^{-1}\equiv-4\equiv67\pmod{71}

d. Same process as with (b). First we have 71\equiv18\pmod{53}, and we've already shown that

1 = 3*18 - 53

which means, taken modulo 53, that

1\equiv3\cdot18\pmod{53}\implies71^{-1}\equiv18^{-1}\equiv3\pmod{53}

You might be interested in
Y squared plus 7y plus 10 over y squared minus 25
klasskru [66]
Y²+7y+10/y²-25 this is the equation now if your looking for the answer it would be

y^4+7y^3-25y^2-175y+10
_________________________
(y+5)(y-5)

sorry if is a little messy
5 0
3 years ago
Before conducting some experiments, a scientist mixes 1/2 gram of Substance A with 3/4 grams of Substance B. If the scientist us
Tju [1.3M]

Answer: 10

<u>Step-by-step explanation:</u>

 (\frac{1}{2}+\frac{3}{4})÷\frac{1}{8}

= (\frac{1}{2}(\frac{2}{2})+\frac{3}{4})÷\frac{1}{8}

= (\frac{2}{4}+\frac{3}{4})÷\frac{1}{8}

= (\frac{5}{4})÷\frac{1}{8}

= (\frac{5}{4})x\frac{8}{1}

= \frac{40}{4}

= 10

4 0
3 years ago
Find the Slope of the line through each pair of points: (-4,11),(1,-9)
kogti [31]

Answer:

rise/run= -20/5= -4/1=-4 slope

or you sound use the slope formula (y2-y1)/(x2-x1)

(-9-11)/(1+4)

-20/5

-4

Step-by-step explanation:

6 0
3 years ago
Before leaving to visit Mexico, Levant traded 270 American dollars and received 3,000 Mexican pesos. When he returned from Mexic
erica [24]

The amount of dollars that Mr. Levant would exchange for 100 pesos on his return is <u>$9</u>.

<h3>What is an exchange rate?</h3>

An exchange rate is a rate that is used to convert one nation's currency to another.

The exchange rate is based on the purchasing power of each nation's currency.

<h3>Data and Calculations:</h3>

Dollars before traveling to Mexico = $270

Value of Mexican pesos received for $270 = 3,000 pesos

Exchange rate = $1 = 11.11 pesos (3,000/$270)

Amount of pesos left after the trip = 100 pesos

Value of 100 pesos in dollars = <u>$9</u> (100/$11.11)

Thus, the amount of dollars that Mr. Levant would exchange for 100 pesos on his return is <u>$9</u>.

Learn more about exchange rates at brainly.com/question/2202418

#SPJ1

4 0
2 years ago
Jessica just put 14.41 gallons of fuel into her car. There were 3.6 gallons in the car to begin with. How much fuel is in jessic
SIZIF [17.4K]

Answer:

18.01 gallons

Step-by-step explanation:

14.41

3.6

=18.01

8 0
3 years ago
Other questions:
  • Please help me with problem 2 of graphs
    9·2 answers
  • Can someone help me with 2-5?
    6·1 answer
  • The number of people In Pinellas county has been increasing at a rate of 1.3 percent per year. In 2016, there were 960,730 peopl
    9·1 answer
  • Mr.Winston is adding a sunroom to his house. After laying the foundation and building the frame he double checks his measurement
    10·1 answer
  • I keep getting 13.4 which I'm not sure is right. ​
    5·2 answers
  • Please help me with this math assignment!
    8·1 answer
  • How do you write 0.8959 as a percentage?
    13·2 answers
  • a onion is 0.6 pounds and the cost of that onion is $0.48 what is independent and dependent variables
    10·1 answer
  • COME ON PLEASE HELP ME A FRICKING CRYING PLEASE HELP
    14·1 answer
  • Determine whether or not each of the following is a partition of set N of natural numbers. (With reason)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!