Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / C / C2 / v

Table of contents
- Solution v

Solution

Euler's criterion gives

(- 1/ p) = (- 1)^{(p - 1) /2}

. The Legendre symbol is multiplicative, so multiplying this sign by the result of (iv) yields

(\frac{- 2}{p}) = {1, - 1, p \equiv 1, 3 (mod 8), p \equiv 5, 7 (mod 8) .

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