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).
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Find all solutions to the following linear congruences. (15
points)
(a) 2x ≡ 5 (mod 7)....
A) If possible, solve the following system of congruences using either of the two methods of...
A) If possible, solve the following system of congruences using either of the two methods of this section. x ≡ 4 (mod 11) x ≡ 3 (mod 17) x ≡ 6 (mod 18) B) Find the inverse of 19 modulo 23. Show all steps taken in neat English to receive a positive review
(3) Solve the following linear congruence: 271 = 12 mod 39. (4) Solve the following set...
(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.
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
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
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA"...
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 1)) (5, 24) 1. 6. [5 points each (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base...
Show all the steps: 42^7 mod 253 = 15 (5*269) mod 336 =27
Show all the steps: 42^7 mod 253 = 15 (5*269) mod 336 =27
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
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...
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and...
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
(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.
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
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 1)) (5, 24) 1. 6. [5 points each (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base...
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
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
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