Please show question 1 (all parts). Thank you!
Please show question 1 (all parts). Thank you! 1. Using the Euclidean algorithm to find the...
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...
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....
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).
Question 1. (a) Find the greatest common divisor of 10098 and 3597 using the Euclidean Algorithm. (b) Find integers a and a2 with 1009801 +3597a2 = gcd(10098,3597). (c) Are there integers bı and b2 with 10098b1 + 3597b2 = 71? Justify your answer. (d) Are there integers ci and c2 with 10098c1 + 3597c2 = 99? Justify your answer. Question 2. Consider the following congruence. C: 21.- 34 = 15 (mod 521) (a) Find all solutions x € Z to...
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
1. (15 points) Use the Euclidean Algorithm to find GCD(344,72). Note: You must show all major steps of the algorithm to derive your answer.
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.)
Numbers 3,4,11 a. SublactiTlnb b. division of nonzero rationals c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with integer entries e. exponentiation of integers 3. Which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with real entries e. exponentiation of integers 4. Which of the following sets are closed...
PLEASE ANSWER ALL PARTS AND SHOW WORK. THANK YOU! Find the point on the graph of z = -22 - y2 - ty that is the farthest above the plane 5x + 4y + z = -3 (use vertical distance, not overall distance). How far above the plane is that point? Select one: a. 12 b. 5 C. 3 d. 10 e. 7 If X and Y have joint density function 8xy if 0 < x <1, 0 < y...
Please show all work and answer all parts of the question. Please do not repost the question and if you do please at least include the actual code and not the written answer that is incorrect to other posts. Consider the initial boundary value problem (IBVP) for the 1-D wave equation on a finite domain: y(0,t) 0, t > 0 t > 0 y(1,0) f(x) where f(x) =-sin ( 2 π-π (a) Plot the initial condition f(x) on the given...