 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/c/c2/a/i/solution

a

p

(\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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