(3) Solve the following linear congruence: 271 = 12 mod 39. (4) Solve the following set...
Arrange the steps in the correct order to solve the system of congruences x 2 (mod 3), x 1 mod 4). and x3 (mod 5) using the method of back substitution Rank the options below Thus, x= 31.2 - 3/4 + 1)2 - 120+5 We substitute this into the third congruence to obtain 12.5 13 mod 5), which implesu li imod 5) Hence, w5v4 and so x 12.5 - 12/5 + 4) - 5 - 60v. 53, where vis an...
12. Solve the congruence 2x = 7 (mod 17).from discrete math and its appl.chap 3.7 # 12
Problem 2. Solve the congruence equation x( 12 mod 143 Problem 2. Solve the congruence equation x( 12 mod 143
Solve the system of congruencesx= 4 (mod 6)x= 13 (mod 15)
9. Use the construction in the proof of the Chinese remainder theorem to find a solution to the system of congruences X 1 mod 2 x 2 mod 3 x 3 mod 5 x 4 mod 11 10. Use Fermats little theorem to find 712 mod 13 11. What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 (4xn + 1) mod 7 with seed xo 3? 9. Use the construction in the proof of the Chinese...
Find all solutions to the following linear congruences. (15 points) (a) 2x ≡ 5 (mod 7). (b) 6x ≡ 5 (mod 8). (c) 19x ≡ 30 (mod 40). Show all the steps taken in neat English to receive a positive review
2. For each of the following, find all integers a with 0 S < n, satisfying the following congruences modulo n. (a) 3x5 (mod 7) (b) 3x 5(mod 6) (c) 3x 3(mod 7) (d) 3 3 (mod 6) (e) 2x 3(mod 50) (f) 22r 15(mod 67) (g) 79x 12 (mod 523) 2. For each of the following, find all integers a with 0 S
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....
solve each of the following linear congruences using Euler's Theorem.a) 5x≡3 (mod 14)b)4x≡7 (mod 15)c) 3x≡5 (mod16)
Which two is true as i'm confusedA) 3+7 佭 10 mod 15 17 + 9 佭 4 mod 21 12 + 14 佭 0 mod 26B) 4+11 佭 2 mod 13 9+7 佭 4 mod 1213 + 13 佭 1 mod 25 C) 5+9 佭 4 mod 10 16 + 13 佭 3 mod 26 12 + 7 佭 6 mod 14d)2+7 佭 9 mod 15 15 + 15 佭 6 mod 22 8+5 佭 2 mod 10e)7+11 佭 1...