Arrange the steps in the correct order to solve the system of congruences x 2 (mod...
5. (20 points) Solve the system of congruences x (mod 13) and 11 (mod 24). Find the smallest nonnegative integer solution to the system.
(a) Solve the simultaneous congruences p = 1 (mod x – 3), p = 7 (mod x – 5). (b) Find the total number of monic irreducible polynomials of degree 5 in Fr[c]. (c) Find a primitive root modulo 52020. (Make sure to justify your answer.) (d) Determine the total number of primitive roots modulo 52020.
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...
If we assume that x is very small compared to 0.00250, the first iteration gives x=(0.00250×4.5×10−4)1/2=0.00106. Even though the assumption is not valid, it seems likely that [HNO2] is closer to (0.00250−0.00106)M than to 0.00250 M. Substitute the new value into the original equation to obtain the second iteration, x20.00250−0.00106=4.5×10−4 and then x=8.04×10−4. Now, we can restrict x to the following range: 8.04×10−4<x<1.06×10−3 Use the new value of x to write that [HNO2]=(0.00250−0.000804)M and solve the equation once again for...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
Write code for RSA encryption package rsa; import java.util.ArrayList; import java.util.Random; import java.util.Scanner; public class RSA { private BigInteger phi; private BigInteger e; private BigInteger d; private BigInteger num; public static void main(String[] args) { Scanner keyboard = new Scanner(System.in); System.out.println("Enter the message you would like to encode, using any ASCII characters: "); String input = keyboard.nextLine(); int[] ASCIIvalues = new int[input.length()]; for (int i = 0; i < input.length(); i++) { ASCIIvalues[i] = input.charAt(i); } String ASCIInumbers...
I have to use the following theorems to determine whether or not it is possible for the given orders to be simple. Theorem 1: |G|=1 or prime, then it is simple. Theorem 2: If |G| = (2 times an odd integer), the G is not simple. Theorem 3: n is an element of positive integers, n is not prime, p is prime, and p|n. If 1 is the only divisor of n that is congruent to 1 (mod p) then...
Please help me solve this question using Excel data!! (attached on bottom) Thank you!!! Question 2 5 pts Continuing with our data visualization, create a scatterplot with the total number of check-ins (TotCheckins) on the y-axis and the average ratings (AvgRating) on the x-axis. Be sure that the equation for the trend line and the r value are shown on the scatterplot. While your plot may be different aesthetically, which of the following is an accurate representation of the data?...
1. Kinetics is the study of forces acting on a system. True False 2. Kinematics is the study of motion without regard to its causes (forces). True False 3. The similarity between the Macrocycle Flowchart, the Training Pyramid and the Goals for Performance pyramid can be best described as an athlete should have a structured foundation and not proceed too early. True False 4. When should static stretching be performed? Minutes before event performance Hours prior to event or the...
Given the value line: a.) what is the top line growth for 2015? b.)Bottom-Line? c.) Annual dividen per share? d.) Current ratio in 2014? e.) % bonds of Captial structure f.) p/e ratio g.) beta h.) EBITDA % I.) Long-Debt % change 2015 We were unable to transcribe this image41.65 TO 20.1 (Media 92) ATM 1.12 ** 3.4% YAKE 1965 07 2:22. 87 3. 35.8 COCA-COLA NYSE:KO TIMELINESS 4 Lowered 70115 h: 289 29 SAFETY . 1 New 727190 LEGENDS...