4. (4 points) Express ged(10001, 13422) = 1 as a linear combination of 10001 and 13422...
2,3,4,5,6 please
2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482, 7633) 3. Prove that if a = bq+r, then ged(a, b) = ged(b,r). such that sa tb ged(a,b) for the following pairs 4. Use Bézout's theorem to find 8 and a. 33, 44 b. 101, 203 c. 10001, 13422 5. Prove by induction that if p is prime and plaja... An, then pla, for at least one Q. (Hint: use n = 2 as...
20 points Problem 4: Extended Euclidean Algorithm Using Extended Euclidean Algorithm compute the greatest common divisor and Bézout's coefficients for the pairs of integer numbers a and b below. Express the greatest common divisor as a linear combination with integer coefficients) of a and b. (Do not use factorizations or inspection. Please demonstrate all steps of the Extended Euclidean Algo- rithm.) (a) a 270 and b = 219 (b) a 869 and b 605 (c) a 4930 and b-1292 (d)...
1) Use the Euclidean algorithm (write in pseudocode) to find the greatest common divisor of 8 898 and 14 321. 2) Program the Euclidean algorithm in 1) by using C++ programming language. 3) What is the greatest common divisor of 8 898 and 14 321? 4) Next, extend the Euclidean algorithm (write in pseudocode) to express gcd(8 898; 14 321) as a linear combination of 8 898 and 14 321. 5) Continue the programming in 2) to program the Extended...
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...
-2 (1 point) Express the vector v= -6 as a linear combination of x = 5 and - -23 y. x+
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...
Question 6 Express the solution of the following system of equations as a linear combination of complimentary and particular solutions. **( )x+(3) Question 7: Find the particular solution for the following system of differential equations. 6 6t X + on (2010) -10t+4 Question 8: Use Variation of Parameters method to find particular solution for the following system X': 1-3 X + 30 2 -4
Please write neatly and clearly, show all work. Thank you! (I've
been stumped for awhile)
(1 point) Find the smallest positive integer x that solves the congruence: 11x = 4 (mod 68) x = (Hint: From running the Euclidean algorithm forwards and backwards we get 1 = s(11) + +(68). Find s and use it to solve the congruence.)
Please solve the above 4 questions.
1. Using the extended Euclidean Algorithm, find all solutions of the linear congruence 217x 133 (mod 329), where 0 x < 329 (Eg. if 5n, n 0,. ,6) 24 + 5n, п %3D 0, 1, . .., 6, type 24 + x< 11 2. Find all solutions of the congruence 7x = 5 (mod 11) where 0 (Eg. if 4,7 10, 13, type 4,7,10,13, none. or if there are no solutions, type I 3....
Question 10 of 1 Question 10 1 points Let Ybe a linear combination of the random variables X, X, and X3 with C 1. C1, C1. Note that CC, and are the coefficients of the linear combination of X, X, and X, are independent, then the following is true VM-C1-C2 C3 The Covariance of 04-05 VY-VX1) - VDX) VD<3) The answer is not listed