The answers of the above expressions are :
a) 19 mod 3 = 1
b) -19 mod 3 = 2
c) -20 mod 3 = 1
d) ⌊-7.6⌋ = -8
e) ⌈-7.6⌉ = -7
PROBLEM 5 [points: 10] Find values: a) 19mod 3 = b) -19 mod 3 = c)...
4. Find each of these values: (a) (177 mod 31 + 270 mod 31) mod 3 (b) (177 mod 31 · 270 mod 31) mod 31
(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...
5. (20 points) Solve the system of congruences x (mod 13) and 11 (mod 24). Find the smallest nonnegative integer solution to the system.
Problem 5 1. Find the values of (379) and (4725). 2. Prove that for any m > 2, (m) is even. 3. Prove that if (371) - 36(n) then 3|n. Hint: Try proving the contrapositive. 4. Suppose that a =b (mod m), a = b (mod n), and ged(m, n) = 1. Prove that a = b (mod mn). 5. Use Euler's Theorem and the method of successive squaring to find 56820 (mod 2444). That is, find the canonical residue...
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
part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulative distribution fpaction of (e) What is the probability that, of 3 of these lampe, at keast 2 will function for at least 15 hours? Assume that the 3 lamps function/fail independent of each other 7 Problem 4. (15 points) The...
302 i(t) Problem 5(20 points) For the circuit on the right: (a) Find the current ift) in the 3-2 resistor in the form i(t) = lalu (b) Calculate the average and rms values of iſt). (c) Calculate the power dissipated in the 3-2 resistor (d) Find the active power of current source 14 V 50cos (2000) 240 mit
19) How many significant figures are in 1009.630 mL? A) 3 B) 4 C) 5 D) 6 E) 7 F) 8 20) How many different values of my are possible in the 4f sublevel? A) 1 B) 3 C) 5 D) 7 E) 9 F) 11
comute the following (a) 55555555 mod 5555 (b) 77766 mod 5 (c) Let n be a composite integer bigger than 4, compute n-1 i mod n i=1
Problem 3 1. Find the values of (379) and (4725). 2. Prove that for any m > 2, (m) is even. 3. Prove that if (371) - 36(n) then 3|n. Hint: Try proving the contrapositive. 4. Suppose that a =b (mod m), a = b (mod n), and ged(m, n) = 1. Prove that a = b (mod mn). 5. Use Euler's Theorem and the method of successive squaring to find 56820 (mod 2444). That is, find the canonical residue...