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1. Find a solution to each of the following congruences (you might need a calculator): r'...
Discrete structure For each of the following congruences if there is a solution, express the solution...
Discrete structure For each of the following congruences if there is a solution, express the solution in the form x ≡ some_number (mod some_modulus), e.g. x ≡ 6 (mod 9). To standardize answers, some_number should always be a value in the range {0, 1, 2, ..., some_modulus -1}. For example x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not. If there is no solution say "No solution". You don't have to show work for any of the...
please help！！！ Discrete Structures For each of the following congruences if there is a solution, express...
please help！！！ Discrete Structures For each of the following congruences if there is a solution, express the solution in the form x ≡ some_number (mod some_modulus), e.g. x ≡ 6 (mod 9). To standardize answers, some_number should always be a value in the range {0, 1, 2, ..., some_modulus -1}. For example x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not. If there is no solution say "No solution". You don't have to show work for any...
(1 pt) Solve each of the following congruences. Make sure that the number you enter is...
(1 pt) Solve each of the following congruences. Make sure that the number you enter is in the range 10, M – 1 where M is the modulus of the congruence. If there is more than one solution, enter the answer as a list separated by commas. If there is no answer, enter N. (a) 38.r = 1 (mod 273) x= (b) 183.x = 123 (mod 273) x =
Find all solutions to the following linear congruences. (15 points) (a) 2x ≡ 5 (mod 7)....
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 congruen...
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
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 fin...
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...
How many classes of solutions are there for each of the following congruences? (a) x2 -...
How many classes of solutions are there for each of the following congruences? (a) x2 - 1 = 0 mod (168) (b) x2 + 1 = 0 mod (70) (c) x2 + x + 1 = 0 mod (91) (d) x3 + 1 = 0 mod (140) Please note to show how you got the solutions as well as finding out how many classes of solutions there are for each congruence. Please explain every step so I can understand how...
7) Determine if the following congruences have solution(s) and find the solutions if they exist: a....
7) Determine if the following congruences have solution(s) and find the solutions if they exist: a. 22x = 4 mob 29 b. 51x = 21 mob 36 C. 35x = 15 mod 182 d. 131x = 21 mob 77 e. 20x = 16 mob 64
3. (16 points) Solve the system of linear congruences using the Chinese Remainder Theorem. 4 (mod...
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?
Find all the integers x which are the solutions to the following congruences. x^2 is equivalent...
Find all the integers x which are the solutions to the following congruences. x^2 is equivalent to 2 mod 17
(1 pt) Solve each of the following congruences. Make sure that the number you enter is in the range 10, M – 1 where M is the modulus of the congruence. If there is more than one solution, enter the answer as a list separated by commas. If there is no answer, enter N. (a) 38.r = 1 (mod 273) x= (b) 183.x = 123 (mod 273) x =
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
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...
7) Determine if the following congruences have solution(s) and find the solutions if they exist: a. 22x = 4 mob 29 b. 51x = 21 mob 36 C. 35x = 15 mod 182 d. 131x = 21 mob 77 e. 20x = 16 mob 64
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?
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