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
The Grand Canyon is approximately 2^9 kilometers long. Mariner valley is a canyon on mars that is approximately 2^12 kilometers
gulaghasi [49]
2^12 - 2^9 would equal 3,584 
3 0
3 years ago
Write the log equation as an exponential equation
Serjik [45]

Answer:

(z+5)^{(3x+4)}  = 9

Step-by-step explanation:

Tip: When log_{a} b = c, a^{c} =b is also true.

log_{z+5} (9) = 3x+4   | <em>Original equation</em>

(z+5)^{(3x+4)}  = 9      | <em>Use tip</em>

7 0
3 years ago
Read 2 more answers
Anyone know this ? Math
ziro4ka [17]

Answer:

line r or MB

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
3.0 plzzzzzz help thank you
hoa [83]

Answer:

80%

Step-by-step explanation:

100/5*4

8 0
3 years ago
Does this graph show a function? Explain how you know.
torisob [31]

Answer:

A

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • You invest $300 in an account that has an interest rate of 1.3%, compounded monthly. How much money is in the account after 10 y
    7·1 answer
  • A prism is filled with 44 cubes with 0.5-unit side lengths. What is the volume of the prism in cubic units?
    10·1 answer
  • Erin and Ethan add the fractions 2 1/3 and 1 1/6. Look at their work below
    9·1 answer
  • How much more of his allowance did Nathan spend on the
    14·1 answer
  • 2. Mrs. Adams wants to buy bags of candy to pass
    12·1 answer
  • PLS HELP AND EXPLAIN THIS I GOT 10 minutes leftttt...
    6·2 answers
  • F(x) = x2+ x–1 and g(x) = x+ 3, what is f o g(x)
    5·1 answer
  • Isosceles triangle ABC contains angle bisectors BF. AD and CE that intersect at X
    8·1 answer
  • What is x if 3x+6= 39
    8·2 answers
  • (04.03) The graph shows the amount of money paid when purchasing bags of candy at the zoo:
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!