 Solution

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

For distinct odd primes

p, q

(p / q) (q / p) = (- 1)^{\frac{p - 1}{2} \frac{q - 1}{2}} .

Thus the two symbols have opposite signs exactly when both primes are three modulo four; otherwise they agree. Distinctness excludes zero symbols.

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