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Mathematics and philosophy course of the University of Oxford

Year 2 of the mathematics and philosophy course of the University of Oxford

Options II for mathematics and philosophy course of the University of Oxford

Past exam of the options II for mathematics and philosophy course of the University of Oxford

2013

The <first supplementary law for quadratic reciprocity> is
$$
\boxed{(-1/p)=(-1)^{(p-1)/2}=\begin{cases}1,&p\equiv1\pmod4,\\-1,&p\equiv3\pmod4.\end{cases}}
$$
It also follows immediately from <Euler's criterion> applied to $-1$.

Solution

Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / C2 / a / ii / Solution

Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / C2 / a / ii / Solution

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Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / C2 / a / ii / Solution

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