 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2004/c/c2/a/ii/solution

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

For

p ∤ a

the right side is

+ 1

- 1

. The displayed congruence also holds for

p ∣ a

, since

p

is odd and the exponent is positive.

 New to topics? Read the docs here!