 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2015/1/a/iii/solution

p, q

(\frac{p}{q}) (\frac{q}{p}) = (- 1)^{(p - 1) (q - 1) /4} .

Thus the two Legendre symbols agree unless both prime numbers are congruent to

3

4

, in which case they have opposite signs.

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