Past exam of the short options course of the University of Oxford / 2021 / 1 / a / ii

Table of contents
- Solution ii

Solution

Factor

Q = \prod_{i} p_{i}

and

Q^{'} = \prod_{j} q_{j}

, retaining repeated prime factors. If

P

has a common prime factor with

Q Q^{'}

, it has one with at least one of

Q, Q^{'}

, and both sides of the desired equality are zero. Otherwise the definition of the Jacobi symbol gives

(\frac{P}{Q Q ^{'}}) = i \prod (\frac{P}{p _{i}}) j \prod (\frac{P}{q _{j}}) = (\frac{P}{Q}) (\frac{P}{Q ^{'}}) .

An empty product is

1

, so the argument includes either denominator being

1

.

 Ancestors (12)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version