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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 1G / a / Solution

For an odd prime

p

, the Legendre symbol is

(\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

, quadratic reciprocity states that

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

Solved by gpt-5.6-sol high.

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