Question: (1) This question is about quadratic equations. (a) Solve the quadratic equation: x = 531 (mod 2021) (12 marks). (b) Use the Legendre or

$(1) This question is about quadratic equations. (a) Solve the quadratic equation: ( x^{2} equiv 531 ) (mod 2021) (12 marks$

(1) This question is about quadratic equations. (a) Solve the quadratic equation: x = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x = 1097 (mod 65539). Give an answer. Note: You don't have to solve the quadratic equation; you need to only determine if it has a solution or not. (c) Verify the answer of each equation in sagemath. (1+1 marks) (1) This question is about quadratic equations. (a) Solve the quadratic equation: x = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x = 1097 (mod 65539). Give an answer. Note: You don't have to solve the quadratic equation; you need to only determine if it has a solution or not. (c) Verify the answer of each equation in sagemath. (1+1 marks)

Step by Step Solution

★★★★★

3.34 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

to As per legendres symbol for relationship in quadradic say that if x solution for ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Using data from 50 workers, a researcher estimates Wage = 0 + 1Education + 2Experience + 3Age + , where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher...

The data shown in the following table were obtained from the 1990 Census. Included is information on 26 randomly selected Metropolitan Statistical Areas (MSAs). Of interest are factors that...

The data shown in the following table related to the concealed weapons permits issued in 13 randomly selected Florida counties in 1996. (a) Test whether the data are normal. (b) If not, try a...

please solve and answer all this question asap i will give thumbs up Consider the nonlinear equation f(x)=0 which we know has a solution x in the interval [0,1] (e.g. by using the Intermediate Value...

+ X m125 - Section 3.9 (2021) - Math VA X Feedback fo webassign.net/web/Student/Assignment-Responses/last?dep=2786834 4 Points] DETAILS One use of linear approximation is to solve certain equations...

Lab Assignment Objectives Be able to recognize a situation in which a subtask is a simpler version of the larger problem and design a recursive solution to solve this problem. Safeguard against...

Note: All ML code must be explained clearly (INJAVAXX)and should be free of needless complexity. 2 CST.2016.1.3 2 Foundations of Computer Science Please help. (2c) (a) A prime number sieve is an...

Digital Electronics An arbiter is a functional unit that allows requesters to lock resources while they are in use. (a) Describe the inputs and outputs of an arbiter for a single resource which has...

1 of 9 LYS Math 2412 - Final Exam Review Problems Update:11/18/ 1. Verify the identity: tan(x) sin(x) + cos(x) = sec(x) 2. Verify the identity: sin(x) - sin(x) cos2(x) = sin(x) 3. Verify the...

In 2020, Maggy (34 years old) is an employee of YBU Corp. YBU provides a 401(k) plan for all its employees. According to the terms of the plan, YBU contributes 50 cents for every dollar the employee...

Below are the transactions for Button Sewing Shop for March, the first month of operations. March 1 Issue common stock in exchange for cash of $2,600. March 3 March 5 March 7 Purchase sewing...

What idea justifies employers being conscious of employees working too many long hours? a.) Employees working long hours can be counterproductive to a firm. b.) Constant disengagement by employees...

CC13-1 Evaluating Profitability, Liquidity, and Solvency [LO4, L05) Looking back over the past few years, it is clear that Nicole Mackisey has accomplished a lot running her business, Nicole's...

" 2.7 HW X + es/24606/assignments/509305 Megan is an industrial engineer for Coyner Cola Company. She takes a random sample of cola cans from the production line each day to determine if the product...

I need some help with question 8 of case 1. The book tilte is: Cases in Financial Management. Authors: John S Dunkelberg and Joseph M Sulock B. (a) Suppose Studebaker's goal is to accumulate $400,000...

Which statement is INCORRECT about pseudo probabilities? They are not actual/real probabilities They are also called martingale probabilities They are expected probabilities of stock of going up and...

Write each fraction as a percent. 7 50

A researcher interviews 50 employees of a large manufacturer and collects data on each workers hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The entire data...

Construct the null and the alternative hypotheses for the following claims: a. I am going to get the majority of the votes to win this election. b. I suspect that your 10-inch pizzas are, on average,...

Jane Wormley is a professor of management at a university. She expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5%...

The comparative statements of financial position of Menachem NV at the beginning and end of the year 2019 appear below. Net income of 34,000 was reported, and dividends of 23,000 were paid in 2019....

The current assets and current liabilities sections of the statement of financial position of Jin Liu Ltd. appear as follows (amounts in thousands). The following errors in the company's accounting...

The comparative statements of financial position of Lopez Inc. at the beginning and the end of the year 2019 appear as follows. Net income of $34,000 was reported, and dividends of $13,000 were paid...