(1) This question is about quadratic equations. (a) Solve the quadratic equation: :02 E 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con gruence has a solution: x2 E 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) 12+10+2=24 marks Part (a) The student receives 12 marks if all the steps of the computation are correct and he/she gives an answer. This includes 2 marks for transforming the equation into four systems of linear equations, 2 marks for solving each of the four systems, and 1 mark for giving a nal answer. Also, the student gets 1 mark for applying at least once the extended Euclidean algorithm. For different level of correctness the student receives between 11 and 0 marks. Part (b) The student receives 1 mark for each correctly justied step in his/ her an- swer, up to ten steps. The nal answer is worth 1 mark. For different level of correctness the student receives between 9 and 0 marks. Part (c) The student receives 1 mark if a correct sagemath code is provided