Find (i) 2^25 mod 21, (ii) 7^66 mod 120 and (iii) the last two digits of...
Find (i) 2^25 mod 21, (ii) 7^66 mod 120 and (iii) the last two digits of 1 + 7^162 + 5^121 * 3^312
Homework Answers
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Find (i) 2^25 mod 21, (ii) 7^66 mod 120 and (iii) the last two
digits of...
6.) Find (i) 225 mod 21, (ii) 766 mod 120 and (iii) the last two digits...
6.) Find (i) 225 mod 21, (ii) 766 mod 120 and (iii) the last two digits of 1 + 7162 + 5121. 3.12. 6. Find + (iii) the last two digits of 1 + 7162 +5121.3.12 (i) 225 mod 21, (ii) 766 mod 120 Answ ven 6. (i) 225 = 2 mod 21; (ii) 766 = 72 = 49 mod 1 20. (iii) °(100) = 40. So the last two digits of 7162 are 49. Note that, since (5, 100)...
Evaluate the following: (i) 7^1300 mod 8, (ii) 72^36 mod 15, (iii) 15^546 mod 17. You...
Evaluate the following: (i) 7^1300 mod 8, (ii) 72^36 mod 15, (iii) 15^546 mod 17. You may not use a calculator or computer - do this by hand, and show your computations.
Q1. Consider the curve y2 = x3 + 3x + 5 mod 17. (i) (ii) (iii)...
Q1. Consider the curve y2 = x3 + 3x + 5 mod 17. (i) (ii) (iii) (iv) (v) (vi) Confirm that it is an elliptic curve. Determine three points on the curve over real numbers Determine three points on the curve over integer numbers For one of the points P in (iii), find 2P (or double) For two of the points P and Q in (iii), find P+Q Find the bound for the number of points on this curve using...
5. What is (i) 1 + 10 + 100 + 1000 + 1000000 + 100000000000 mod...
5. What is (i) 1 + 10 + 100 + 1000 + 1000000 + 100000000000 mod 2? (ii) 1+ 7 + 72 + 73 + 74 + 710 + 7100 mod 7? (iii) What is 17.33 +81 · 98 mod 6? 6. Solve each of the following equations for the unknown variable X = 0,1,2, 3, 4, 5, 6 mod 7. (i) 2X + 5 = 6 mod 7. (ii) 3X + 5 = 6 mod 7.
Find the last two digits of . How do I know phi(100) = 2^2 * 5^2...
Find the last two digits of . How do I know
phi(100) = 2^2 * 5^2 *(1- 1/2)* (1-1/5) ???? This appears and feels
it has been done out of thin air. Then, Fermitas ?!?
How to use the previous answer of 1 a) i ii iii to find the eigenvalue...
How to use the previous answer of 1 a) i ii iii to find the
eigenvalue from iv
Mock Exam 2019 SEM 1 1. (a) Given the system of linear equations x- 2y +2z= 1, 2x+y+ 5z = 7, 2x-9y3z = -3 i. Write the system in augmented matrix form [A -b) and apply Gaussian elimination to reduce this to row echelon form. ii. Identify the basic and free variables iii. Write down the solution space for this system of...
Write the following rectangular points in polar coordinates. i. (0.1) ii. (5,5) 333 iii. 21 2...
Write the following rectangular points in polar coordinates. i. (0.1) ii. (5,5) 333 iii. 21 2 iv. (-6, 0) v. (9, -3)
19. Which of the following molecules are achiral? A) II, III B) I, II C) I, IV D) III, IV 20. How many stereogenic...
19. Which of the following molecules are achiral? A) II, III B) I, II C) I, IV D) III, IV 20. How many stereogenic centers are present in ephedrine, a bronchodilator and decongestant? ephedrine A) 0 B) 1 C) 2 D) 3 21. Rank the following groups in order of decreasing priority according to the Cahn-Ingold- Prelog system. -NH2 -NHCH3 -CH2NH2 CH2NHCH3 п V . A) B) I>II> III > IV II >I>IV > III II C II >I> III...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
The expression can be rewritten in different ways. Which of (i), (ii), (iii) below have the...
The expression can be rewritten in different ways. Which of (i), (ii), (iii) below have the same numerical value as 3 ? 3 in (8)(7)(6) (3)(2) (i) (ii) (iii) 5 5! A. (i) and (ii) only OB. (i) and (iii) only Oc.(ii) and (iii) only OD. (i) only O E. (ii) only Reset Selection
6.) Find (i) 225 mod 21, (ii) 766 mod 120 and (iii) the last two digits of 1 + 7162 + 5121. 3.12. 6. Find + (iii) the last two digits of 1 + 7162 +5121.3.12 (i) 225 mod 21, (ii) 766 mod 120 Answ ven 6. (i) 225 = 2 mod 21; (ii) 766 = 72 = 49 mod 1 20. (iii) °(100) = 40. So the last two digits of 7162 are 49. Note that, since (5, 100)...
Q1. Consider the curve y2 = x3 + 3x + 5 mod 17. (i) (ii) (iii) (iv) (v) (vi) Confirm that it is an elliptic curve. Determine three points on the curve over real numbers Determine three points on the curve over integer numbers For one of the points P in (iii), find 2P (or double) For two of the points P and Q in (iii), find P+Q Find the bound for the number of points on this curve using...
5. What is (i) 1 + 10 + 100 + 1000 + 1000000 + 100000000000 mod 2? (ii) 1+ 7 + 72 + 73 + 74 + 710 + 7100 mod 7? (iii) What is 17.33 +81 · 98 mod 6? 6. Solve each of the following equations for the unknown variable X = 0,1,2, 3, 4, 5, 6 mod 7. (i) 2X + 5 = 6 mod 7. (ii) 3X + 5 = 6 mod 7.
Find the last two digits of . How do I know
phi(100) = 2^2 * 5^2 *(1- 1/2)* (1-1/5) ???? This appears and feels
it has been done out of thin air. Then, Fermitas ?!?
How to use the previous answer of 1 a) i ii iii to find the
eigenvalue from iv
Mock Exam 2019 SEM 1 1. (a) Given the system of linear equations x- 2y +2z= 1, 2x+y+ 5z = 7, 2x-9y3z = -3 i. Write the system in augmented matrix form [A -b) and apply Gaussian elimination to reduce this to row echelon form. ii. Identify the basic and free variables iii. Write down the solution space for this system of...
Write the following rectangular points in polar coordinates. i. (0.1) ii. (5,5) 333 iii. 21 2 iv. (-6, 0) v. (9, -3)
19. Which of the following molecules are achiral? A) II, III B) I, II C) I, IV D) III, IV 20. How many stereogenic centers are present in ephedrine, a bronchodilator and decongestant? ephedrine A) 0 B) 1 C) 2 D) 3 21. Rank the following groups in order of decreasing priority according to the Cahn-Ingold- Prelog system. -NH2 -NHCH3 -CH2NH2 CH2NHCH3 п V . A) B) I>II> III > IV II >I>IV > III II C II >I> III...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
The expression can be rewritten in different ways. Which of (i), (ii), (iii) below have the same numerical value as 3 ? 3 in (8)(7)(6) (3)(2) (i) (ii) (iii) 5 5! A. (i) and (ii) only OB. (i) and (iii) only Oc.(ii) and (iii) only OD. (i) only O E. (ii) only Reset Selection
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