 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2005/c/1/a/ii/solution

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

It applies also when

p ∣ a

. In particular, for a nonzero residue the power is one or minus one according as the residue is a square or a nonsquare.

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