 Solution

ID: past-exam-of-the-options-ii-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/c2/a/ii/solution

(- 1/ p) = (- 1)^{(p - 1) /2} = {1, - 1, p \equiv 1 (mod 4), p \equiv 3 (mod 4) .

It also follows immediately from Euler's criterion applied to

- 1

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