 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2014/1/a/i/solution

p

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

It depends only on the congruence class of the integer

a

. The values

1

and

- 1

distinguish a nonzero quadratic residue from a quadratic nonresidue; zero is a separate case.

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