Question

- 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.

Answer #1

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, 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 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 != −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 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 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 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 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 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 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

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 6 minutes ago

asked 23 minutes ago

asked 25 minutes ago

asked 30 minutes ago

asked 37 minutes ago

asked 37 minutes ago

asked 39 minutes ago

asked 43 minutes ago

asked 46 minutes ago

asked 46 minutes ago

asked 49 minutes ago