Question

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

Answer #1

Express gcd(1591, 3589, 4171) as an integer linear combination
of 1591, 3589, and 4171.

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)

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

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).

A. Find gcd(213486, 5423) by applying Euclid’s algorithm. B.
Estimate approximately how many times faster it will be to find gcd
(213486, 5423) with the help of the Euclid's algorithm compared
with the alroithm based on checking consecutive integers from min
{m,n} down to gcd(m,n). You may only count the number of modulus
divisions of the largest integer by different divisors.

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

Compute gcd(425, 2020) using extended euclidean algorithm

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

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

Recursively computing sums of cubes, cont.
(a)
Use induction to prove that your algorithm to compute the sum of
the cubes of the first n positive integers returns the correct
value for every positive integer input.

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