2,3,4,5,6 please 2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482,...
6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736). 6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736).
Use R language to program Problem 1: Greatest Common Divisor (GCD) Please write two functions, g edi ) and gcdr , which both take two integers a, b and calculates their greatest common divisor (GCD) using the Euclidean algorithm gcdi () should do so using iteration while gcdr () should use recursion. Then write a third function, gcd(), which takes two integers a, band an optional third argument nethod which takes a charater string containing either "iterative" or "recursive", with...
PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find ged(a,b), and to write gcd(a,b) as a linear combination of a and b, i.e. find integers m and n such that gcd(a,b) = am + bn. (a) a = 36, b = 60. (b) a = 12628, b = 21361. (c) a = 901, b = -935. (d) a = 72, b = 714. (e) a = -36, b = -60.
1 For each of the following pairs of numbers a and b, calculate and find integers r and s such ged (a; b) by Eucledian algorithm that gcd(a; b) = ra + sb. ia= 203, b-91 ii a = 21, b=8 2 Prove that for n 2 1,2+2+2+2* +...+2 -2n+1 -2 3 Prove that Vn 2 1,8" -3 is divisible by 5. 4 Prove that + n(n+1) = nnīYn E N where N is the set of all positive integers....
Please show question 1 (all parts). Thank you! 1. Using the Euclidean algorithm to find the ged of following pairs. Write down the ged as a linear combination of given pairs (a) 524 and 148 in Z (b)33 + 2r +1 and 2 +1 in Zs[] (c) 3 +2r +1 and 1 n Z[] 2. Compute 42001 in Z5 3. Use principal of induction show that 10" 1 mod 9 4. Show that every odd integer is congruent to 1...
T'he goal of this problem is to establish the following remarkable result: Bezout's theorern. If a, be Z50, then 3x, y є Z such that gcd(a, b) = ax + by. Here ged(a, b) denotes the greatest common divisor of a and b (i.e. the largest positive integer that divides both a and b). Throughout this problem, we'll use the notation (a) Write down five numbers that live in 2Z +3Z. What's a simpler name for the set 2Z +3Z?...