part-ii/2005-0/

[tripos-comments[bot]]

Part II 2005 Number Theory: 1.I.1H

https://questions.tripos.org/part-ii/2005-0/

[walrus1729]

Solution

This is all bookwork except for the evaluation of the Legendre symbol. Here, we have

$$ \begin{align*} (91/167) &= (7/167)(13/167) \\ &= -(167/7)(167/13) \\ &= -(6/7)(11/13) \\ &= -(-1)(-1) \\ &= -1 \\ \end{align*} $$