Question

a) Use the Euclidean Algorithm to find gcd(503, 302301).

(b) Write gcd(503, 302301) as a linear combination of 38 and 49.

(c) What is an inverse of 503 modulo 302301?

(d) Solve 503x ≡ 2 (mod 302301)

Answer #1

use the Extended Euclidean algorithm (EEA) to write the gcd of
4883 and 4369 as their linear combination

By hand, use the Extended Euclidean algorithm (EEA) to write
the gcd of 4883 and 4369 as their combination.

Using the extended Euclidean algorithm, find the multiplicative
inverse of a. 135 mod 61 b. 7465 mod 2464 c. 42828 mod 6407

Let x =21212121; y = 12121212: Use the Euclidean algorithm to
find the GCD of x and y. Show all steps.

Use Euclid’s GCD algorithm to compute gcd(356250895, 802137245)
and express the GCD as an integer linear combination of the two
numbers.

Q1. Using Euclideanalgorithm find GCD(21, 1500). Show you
work
.Q2. Using Extended Euclidean algorithm find the multiplicative
inverse of 8 in mod 45 domain .Show your work including the
table.
Q3. Determine φ(2200). (Note that 1,2,3,5, 7, ... etc.are the
primes). Show your work.
Q4. Find the multiplicative inverse of 14 in GF(31) domain using
Fermat’s little theorem. Show your work
Q5. Using Euler’s theorem to find the following exponential:
4200mod 27. Show how you have employed Euler’s theorem here

By the Euclidean
algorithm to find gcd(279174, 399399) and gcd(144, 233). Again you
will want a calculator for the divisions, but show your work. How
many steps (applications of the theorem) does each calculation
require?

Use the Euclidean algorithm to find GCD(221, 85). Draw the Hasse
diagram displaying all divisibilities among the numbers 1, 85, 221,
GCD(85, 221), LCM(85, 221), and 85 × 221.
- Now I already found the gcd and the lcm but I forgot how to
draw the hasse diagram
GCD = 17 and LCM =1105

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...

Consider the numbers 130 and 57.
(1) Use Euclid’s algorithm to find the gcd(57, 130).
(2) Find integers x, y so that 57x + 130y = 1.
(3) Find r ∈ {0, 1, , . . . , 130} so that 57r ≡ 1 (mod
129).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 4 minutes ago

asked 15 minutes ago

asked 23 minutes ago

asked 38 minutes ago

asked 41 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago