Elementary Number Theory Chapter 3.3 Page 54, Why choose "$N = 4q_{1}q_{2} \cdots q_{s} - 1$"?(David M. Burton's 7th Edition)
Why does the author choose $N = 4q_{1}q_{2} \cdots q_{s} - 1$ when proving there are an infinite number of primes of the form $4n + 3$.
Table of Contents
Background
This question arises from David M. Burton's proof for "there are an infinite number of primes of the form $4n + 3$".
Explanation
Why does the author choose $N$ to be $4q_{1}q_{2} \cdots q_{s} - 1$?
Because this can be written in the form of $4n + 3$. Also, it plays an important role when it leads to the contradiction that $r_{i} \mid 1$ as it has the "$-1$" at the end.
Ranblog Newsletter
Join the newsletter to receive the latest updates in your inbox.
){kind=link}