 Solution

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

p ∤ a

, take the least positive residues of

a, 2 a, \dots, ((p - 1) /2) a

p

, and let

s

be the number greater than

p /2

. Then

(\frac{a}{p}) = (- 1)^{s} .

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