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2. Use modular arithmetic rules to find out the following: Use the rule: (a*b) mod x...
Question Lisiaiq a modular arithmetic Compute the following a) –3 mod 5; 9' mad 26; 2t...
Question Lisiaiq a modular arithmetic Compute the following a) –3 mod 5; 9' mad 26; 2t med 9; 8t med 13 6) Find X (smallest) from 9 = 2* (med 11)
Discrete Mathematics. Question 2: (a) Use modular arithmetic to find 1040 mod 210. Show your working....
Discrete Mathematics. Question 2: (a) Use modular arithmetic to find 1040 mod 210. Show your working. (b) An RSA cryptosystem uses public key pq = 65 and e = 7. Decrypt the ciphertext 57 9 and translate the result into letters of the alphabet to discover the message.
Answer the following questions using modular arithmetic a) Determine if 5201,001 −2 is divisible by 3....
Answer the following questions using modular arithmetic a) Determine if 5201,001 −2 is divisible by 3. b) Determine all of the zeros of the polynomial p(x) = x2 + x mod6. c) Show that if a2 + b2 = c2, then a ≡ 0,2 mod 4 or b ≡ 0,2 mod 4
B3 a. Solve for x in this equation: 2x + 11 = 2 (mod 4). b....
B3 a. Solve for x in this equation: 2x + 11 = 2 (mod 4). b. What are the sets of units and zero divisors in the ring of integers modulo 22? (Specify at least the smaller set using set-roster notation.) c. Find a formula for the quotient and the exact remainder when 534 is divided by 8. Hint: find the remainder first by modular arithmetic. Then subtract the remainder from the power and divide to find the quotient.
a. b. c. What does the ciphertext ONL decode to with the modular inverse matrix from Question b? d. We use an encoded...
a.
b.
c. What does the ciphertext ONL decode to with the modular
inverse matrix from Question b?
d. We use an encoded text using a Caesar cipher. The ciphertext
was intercepted which is: THUBYLDH. What is the word? How did you
work this out?
Encode the uppercase letters of the English alphabet as A-0, B-1, C-2 and so on. Encrypt the word BUG with the block cipher matrix 16 4 11] 10 3 2 using modulo arithmetic with modulus...
please answer all the questions. just rearranging. Explanation is not needed. Use modular arithmetic to prove...
please answer all the questions.
just rearranging. Explanation is not needed.
Use modular arithmetic to prove that 3|(221 – 1) for an integer n > 0. Hence, 3|(221 – 1) for n > 0. To show that 3|(221 – 1), we can show that (221 – 1) = 0 (mod 3). We have: (221 – 1) = (4” – 1) (mod 3) Then, (22n – 1) = (1 - 1) = 0 (mod 3) Since 4 = 1 (mod 3),...
2. Find 11644 mod 645 Use the following algorithm and show work! procedure modularExponentiation(b: integer, n...
2. Find 11644 mod 645 Use the following algorithm and show work! procedure modularExponentiation(b: integer, n = (ak-1ak-2...a1a0)2, m:positive integer) x:= 1 power := b mod m for i = 0 to k-1 If ai = 1 then x:= (x⋅power) mod m power := (power⋅power) mod m return x ( x equals bn mod m) Note: in this example m = 645, ai is the binary expansion of 644, b is 11.
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of equations. X 2 7x + 2y - z= -1 ។ 6x + 5y + z = 16 -5x - 4y + 3z = -5 2 : 2 a. Write the coefficient matrix first for the system above. Call it matrix D. 7 2 5 L-8-4 3 1 14 ] = 0 b. Find the determinant of the coefficient matrix (det(D)).
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
Question Lisiaiq a modular arithmetic Compute the following a) –3 mod 5; 9' mad 26; 2t med 9; 8t med 13 6) Find X (smallest) from 9 = 2* (med 11)
B3 a. Solve for x in this equation: 2x + 11 = 2 (mod 4). b. What are the sets of units and zero divisors in the ring of integers modulo 22? (Specify at least the smaller set using set-roster notation.) c. Find a formula for the quotient and the exact remainder when 534 is divided by 8. Hint: find the remainder first by modular arithmetic. Then subtract the remainder from the power and divide to find the quotient.
a.
b.
c. What does the ciphertext ONL decode to with the modular
inverse matrix from Question b?
d. We use an encoded text using a Caesar cipher. The ciphertext
was intercepted which is: THUBYLDH. What is the word? How did you
work this out?
Encode the uppercase letters of the English alphabet as A-0, B-1, C-2 and so on. Encrypt the word BUG with the block cipher matrix 16 4 11] 10 3 2 using modulo arithmetic with modulus...
please answer all the questions.
just rearranging. Explanation is not needed.
Use modular arithmetic to prove that 3|(221 – 1) for an integer n > 0. Hence, 3|(221 – 1) for n > 0. To show that 3|(221 – 1), we can show that (221 – 1) = 0 (mod 3). We have: (221 – 1) = (4” – 1) (mod 3) Then, (22n – 1) = (1 - 1) = 0 (mod 3) Since 4 = 1 (mod 3),...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of equations. X 2 7x + 2y - z= -1 ។ 6x + 5y + z = 16 -5x - 4y + 3z = -5 2 : 2 a. Write the coefficient matrix first for the system above. Call it matrix D. 7 2 5 L-8-4 3 1 14 ] = 0 b. Find the determinant of the coefficient matrix (det(D)).
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
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