List the first 55 positive numbers that

Mafia We 2022-06-05 Answered

List the first 5 positive numbers that are congruent to 5 in modulo 13

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Haidar Ali
Answered 2022-07-21 Author has 4 answers

Let x be a positive number that is congruent to 5 in module 13. Mathematically it can be written as:

x5 mod (13) 

Note that a number x is congruent to 5 mod 13 if and only if x-5 is divisible by 13. It follows that the possible positive numbers for which x-5 is divisible by 13 are as follows:

5,18,31,44,57, . . .

One can check that:

(1)  5-5=0 and 0 is divisible by 13. This shows that:

                            55 mod (13) 

(2) 18-5=13 and 13 is divisible by 13. This shows that:

                            185 mod (13) 

(3) 31-5=26 and 26 is divisible by 13. This shows that:

                            315 mod (13) 

(4) 44-5=39 and 39 is divisible by 13. This shows that:

                            445 mod (13) 

(5) 57-5=52 and 52 is divisible by 13. This shows that:

                             575 mod (13) 

 

The first five positive numbers that are congruent in 5 modulo 13 are:

5,18,31,44,57

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-11-22

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is 1.00×103 s,calculate the average force between the bat and ball during contest.

asked 2021-01-10

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2 kg physics textbook horizontally toward the north shore , at a speed of 5.0 m/s. How long does ittake him to reach the south shore?

asked 2020-11-05

A 0.50 kg ball that is tied to the end of a 1.1 m light cord is revolved in a horizontal planewith the cord making a 30 angle, with the vertical.
image
a) Determine the ball speed.
b) If, instead, the ball is revolved so that its speed is 4.0 m/s,what angle does the cord make with the vertical?
c) If the cord can withstand a maximum tension of 9.1 N, what is the highest speed at which the ballcan move?

asked 2021-02-21

Two small charged objects repel each other with a force F whenseparated by a distance d. if the charge on each object is reducedto one-fourth of its original value and the distance between themis reduced to d/2, the force becomes: 
a) F16 
b) F8 
c) F4 
d) F2 
e)F

asked 2022-04-10
As shown in the title, I want to show that if a rational function satisfies h ( t ) = h ( 1 / t ), then h(t) can be express in the variable 1 + 1 / t, that is, h ( t ) = f ( t + 1 / t ) for some rational function f. Any help is apreciated.
asked 2022-02-02
How do you combine like terms in (5x2+4)(3x+7)+(2x21)?
asked 2021-12-29
Question: If 1/2 of 5 is 3, then what is 1/3 of 10?

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question