 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2009/c/c2/ii/solution

p ∤ a

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

For a multiple of

p

, both the Legendre symbol and that positive power vanish modulo

p

, so the congruence extends to that case as well.

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