 Solution

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

(2/ p) = (- 1)^{(p^{2} - 1) /8} = {1, - 1, p \equiv 1, 7 (mod 8), p \equiv 3, 5 (mod 8) .

The exponent is an integer because every odd square is one modulo eight.

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