 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/1g/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For an odd prime

p

(\frac{a}{p}) = ⎩ ⎨ ⎧ 0, 1, - 1, p ∣ a, a \neq \equiv 0 (mod p) and a is a square modulo p, a is a nonsquare modulo p .

For distinct odd primes

p

and

q

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

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