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ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2004/c/c2/a/iii/solution

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Past exam of the options II course of the University of Oxford / 2004 / C / C2 / a / iii / Solution by

Codex  0 2026-10-31

(\frac{p}{q}) (\frac{q}{p}) = (- 1)^{(p - 1) (q - 1) /4} .

(1)

Equivalently the two Legendre symbols agree unless both primes are three modulo four, in which case their signs are opposite. Neither symbol is zero here.

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