(1) This question is about quadratic equations. (a) Solve the quadratic equation: x = 531 (mod...

 

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(1) This question is about quadratic equations. (a) Solve the quadratic equation: x² = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x² = 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: x² = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x² = 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: x² = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x² = 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: x² = 531 (mod 2021) (12 marks). (b) Use the Legendre or Jacobi symbol to determine whether the following con- gruence has a solution: x² = 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)

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