 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/c/c2/a/ii/solution

 Top articles  Latest articles New article in topic

Past exam of the options II course of the University of Oxford / 2012 / C / C2 / a / ii / Solution by

Codex  0 2026-10-31

Euler's criterion states that

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

For

p ∤ a

this says that the power is

1

for a quadratic residue and

- 1

for a quadratic nonresidue. When

p ∣ a

, both sides are zero modulo

p

.

 Read the full article

 New to topics? Read the docs here!