 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2021/1/a/i/solution

No. Take

P = 2

Q = 9

(\frac{2}{9}) = (\frac{2}{3})^{2} = (- 1)^{2} = 1,

3

are

0, 1

2

9

would reduce to one modulo

3

, which is impossible. A Jacobi symbol of

1

records a product of local signs; it does not assert that every local sign is positive, or that a quadratic congruence is soluble.

 New to topics? Read the docs here!