I'm trying to understand how to use the circle method to derive an asymptotic formula for Waring's Problem. Do so using the circle method developed by Hardy and Littlewood. In doing this, I want to make sure that:
given $P, Q$ natural numbers with $P > 1$ and $Q \ge 2P$, the following intervals don't overlap:
$\{ c: |c- (a/q)| \le 1/(pQ) \}$ where
- $q \le P$
- $1\le a \le q $
- $(a,q) = 1$
Sorry, I can't seem to get Latex commands right. Any insight to this would be helpful, thanks!