 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/c/c1/ii/solution

p ∤ a

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

The same modular congruence holds for

p ∣ a

, with both sides zero.

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