 Solution

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

Again

s = (a / p) \in {1, - 1}

(s / p) = s^{(p - 1) /2}

. If

p \equiv 1 (mod 4)

, the exponent is even and the answer is one. If

p \equiv 3 (mod 4)

, it is odd and the answer is

s

. Hence

(\frac{( a / p )}{p}) = {1, (a / p), p \equiv 1 (mod 4), p \equiv 3 (mod 4) .

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