Question

We say that x is the inverse of a, modulo n, if ax is congruent to...

  1. We say that x is the inverse of a, modulo n, if ax is congruent to 1 (mod n). Use this definition to find the inverse, modulo 13, of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Show by example that when the modulus is composite, that not every number has an inverse.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The smallest positive solution of the congruence ax ≡ 0( mod n) is called the additive...
The smallest positive solution of the congruence ax ≡ 0( mod n) is called the additive order of a modulo n. Find the additive orders of each of the following elements by solving the appropriate congruences: (abstract algebra) (a) 20 modulo 28 (b) 8 modulo 15 (c) 7 modulo 11 (d) 9 modulo 15
Below is an example of key generation, encryption, and decryption using RSA. For the examples below,...
Below is an example of key generation, encryption, and decryption using RSA. For the examples below, fill in the blanks to indicate what each part is or answer the question. Public key is (23, 11) What is 23 called? _______________, What is 11 called?_______________ Private key is (23, 13) What is 23 called?_______________, What is 13 called?_______________ 23 can be part of the public key because it is very hard to _______________ large prime numbers. ENCRYPT (m) = m^e mod...
For each of the following congruences if there is a solution, express the solution in the...
For each of the following congruences if there is a solution, express the solution in the form x ≡  some_number  (mod some_modulus), e.g. x ≡ 6 (mod 9). To standardize answers,  some_number should always be a value in the range {0, 1, 2, ..., some_modulus -1}. For example x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not. If there is no solution say "No solution". You don't have to show work for any of the problems. Type...
Say that x^2 = y^2 mod n, but x != y mod n and x !=...
Say that x^2 = y^2 mod n, but x != y mod n and x != −y mod n. Show that 1 = gcd(x − y, n) implies that n divides x + y, and that this is not possible, Show that n is non-trivial
In this question we show that we can use φ(n)/2. Let n = pq. Let x...
In this question we show that we can use φ(n)/2. Let n = pq. Let x be a number so that gcd(x, n) = 1. Show that x φ(n)/2 = 1 mod p and x φ(n)/2 = 1 mod q, Show that this implies that and x φ(n)/2 = 1 mod n
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix...
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix theorem below and show that all 3 statements are true or false. Make sure to clearly explain and justify your work. A= -1 , 7, 9 7 , 7, 10 -3, -6, -4 The equation A has only the trivial solution. 5. The columns of A form a linearly independent set. 6. The linear transformation x → Ax is one-to-one. 7. The equation Ax...
1. a. For each number n from 1 to 4, compute n4 modulo 5, leaving your...
1. a. For each number n from 1 to 4, compute n4 modulo 5, leaving your answer as a number from 0 to 4. b. Based on your answers in Problem (a), make a guess for the number np−1 (mod p) when p is any prime number and n is a number from 1 to p−1? c. Using your conjecture from part (b), and some properties of exponents, calculate 81 000 000 (mod 11), leaving your answer as a number...
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is...
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is the largest number that divides both a and b. One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax+by for x, y ∈ N. We say that a and b are relatively prime iff gcd(a, b) = 1. Prove that a and n are relatively prime if and...
Here we have the data showing the number of crimes and the amount spent on prevention...
Here we have the data showing the number of crimes and the amount spent on prevention for n = 12 cities. Find the regression equation predicting number of crimes from amount spent for prevention. Also find r2. Number of crimes Amount for prevention 3 6 4 7 6 3 7 4 8 11 9 12 11 8 12 9 13 16 14 17 16 13 17 14
The table below presents three samples of data. If we conduct a hypothesis test for the...
The table below presents three samples of data. If we conduct a hypothesis test for the equality of all three means with the statistical confidence of 90%, what would the value of the Mean Squares Between Groups be? Sample 1 Sample 2 Sample 3 7 11 6 5 8 5 7 11 4 6 7 5 6 13 14 6 13 5 6 12 5 6 11 6 8 8 8 9 7 6 7 6 14 9 7 4...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT