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
Helen [10]
2 years ago
9

Prove that 41 is congruent to 21 (mod 3). Explain using words, symbols, as you wish

Mathematics
1 answer:
Verdich [7]2 years ago
6 0

From the proof of modular congruence below, it has been shown that;

41 ≡ 21 (mod 3).

<h3>How to Solve Modular Arithmetic?</h3>

We want to use the definition of modular congruence to prove that;

41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).

We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.

First, if we recall the definition of modular congruence:

For integers a, b and positive integer m,  

a ≡ b (mod m) if and only if m|a–b

Suppose 41 ≡ 21 (mod 3).

Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.

Thus;

–(41 – 21) = –3k

So

21 – 41 = 3(–k)

This shows that 3|21 – 41.

Thus;

21 ≡ 41 (mod 3) and the proof is complete

Read more about Modular Arithmetic at; brainly.com/question/16032865

#SPJ1

You might be interested in
What is 1 7/9 - 4/9?
Lera25 [3.4K]
1 7/9 - 4/9

Convert 1 7/9 to an improper fraction:

16/9 - 4/9

Subtract the numerators together:

12/9

Convert to a whole number:

1 1/3
7 0
3 years ago
Read 2 more answers
1. Four bags of chips cost $6. 1. What is the cost per bag? 2. At this rate, how much will 7 bags of chips cost?​
77julia77 [94]

Answer:

$1.50  dollars per bag and at that rate it would be $7.50 for 6 bags of chips

Step-by-step explanation:

8 0
2 years ago
Need help will give brainist ​
ikadub [295]
Photomath i use it for my math all the time it gives you the option for how you wanna solve it and shows you how to solve it
3 0
2 years ago
Read 2 more answers
Please answer this worth 10 points<br><br> look in the image plz
Pachacha [2.7K]
1) It’s true because -5 is way smaller than 3. All the negatives are below the 0 and everything below the 0 is lower than everything above the 0.

2) false. it’s false because in order -5 isn’t even close to 3

3) false.. It’s false because when you have those 2 line that are covering the -5 that means it’s “transforming” into a positive number. So therefore it’s would be 5>3 that would make it true.

4) True. it’s true because like I said the to lines mean the absolute value of something. So it’s being switch to a positive number


Hope this helps :)
5 0
2 years ago
Read 2 more answers
determine if the sequence is geometric or arithmetic and find the ratio or difference. -1, 6, -36, 216
andrew-mc [135]
The sequence is an geometric progression;
Nth=a₁r^(n-1)
a₁ is the first term=-1
r=ratio=a₂/a₁=6/-1=-6

Nth=-1(-6^(n-1)

NTh=an

a
₁=-1(-6⁰)=-1
a₂=-1(-6¹)=6
a₃=-1(-6²)=-36
a₄=-1(-6³)=216

therefore this serie is rising at an increasing fast speed, it is an geometric progression.


4 0
3 years ago
Other questions:
  • Ali is quite the baseball player. Forty two percent of her hits are home runs if Ali hit 150 balls last season how many of those
    10·1 answer
  • What's 18y^3-6y^2-63y+21
    8·2 answers
  • what is this answer and please show me how you got it so I can know how you got it.y= 3 <img src="https://tex.z-dn.net/?f=%5Csqr
    11·1 answer
  • You have $2.50. Each sugar-free gumball in a gumball machine costs $0.25. Write and solve and inequality that represents the num
    10·2 answers
  • What what is in equation of the line that passes through the points (-6, -2) and (6,8)
    6·1 answer
  • Y=-1/2x+4 What is the slope of a line parallel to this line?
    13·2 answers
  • A ball rolling down the hill is an example of what type of energy
    12·1 answer
  • Jack is selling holiday ornaments and boxes of candy. Each ornament is $1.50 and
    11·1 answer
  • I need help with these questions (see image). Please show workings.<br>​
    13·2 answers
  • mrs. henein is purchasing cupcakes for her homeroom class. of each cupcake costs $2.25 and she has 31 students in her homeroom c
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!