 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2010/c/1/ii/solution

a^{(p - 1) /2} \equiv (\frac{a}{p}) (mod p) .

For

p ∤ a

, the sign is

+ 1

precisely for a quadratic residue and

- 1

p ∣ a

, both sides are zero.

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