Past exam of the options II course of the University of Oxford / 2012 / C / C2 / a / i

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- Solution i

Solution

For an integer

a

and 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 not a square modulo p .

The value one refers to a nonzero quadratic residue; divisibility by

p

is recorded separately by zero.

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