Problem 1. Solve the following simultaneous congruence using the Chinese Remainder or the substitution method. a:...
Problem 3. Use the Chinese Remainder Theorem to find all congruence classes that satisfy x2 = 1 mod 77.
(3) Solve the following linear congruence: 271 = 12 mod 39. (4) Solve the following set of simultaneous linear congruences: 3x = 6 mod 11, x = 5 mod 7 and 2x = 3 mod 15.
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) x = 2 (mod 7) x = 3 (mod 9) x = 4 (mod 11)
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) r = 2 (mod 7) x = 3 (mod 9) I= 4 mod 11) Answer,
5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt] Find x (between 0 and 2063*6947) such that x 1480 (2063) and x-5024 (6947) b) [4pt] Find x (between 0 and 2063*6947*8233) such that x 1480 (2063), x 5024 (6947) and x- 7290 (8233) 5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt] Find x (between 0 and 2063*6947)...
3. (16 points) Solve the system of linear congruences using the Chinese Remainder Theorem. 4 (mod 11) a 11 (mod 12) x=0 (mod 13) b. (6 pts) Find the inverses n (mod 11), n21 (mod 12), and nz1 (mod 13). Using these ingredients find the common solution a (mod N) to the system. c. (4 pts) 4. (8 points) What is 1!+ 23+50! congruent to modulo 14?
Problem 2. Solve the congruence equation x( 12 mod 143 Problem 2. Solve the congruence equation x( 12 mod 143
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...
In the following, the moduli are not pairwise relatively prime, so the Chinese Remainder Theorem does not apply immediately. First reduce it to a system with relatively prime moduli and then solve it. 7 (mod 12) =13 (mod 18)
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...