# Textbook Notes

## 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) Paid Members Public

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 $4n + 3$.

## Elementary Number Theory Chapter 3.3 Page 54, Why "But $r_{i}$ cannot be found among the listing $q_{1}, q_{2}, ...$"?(David M. Burton's 7th Edition) Paid Members Public

Elementary Number Theory Chapter 3.3 Page 54, Why "But $r_{i}$ cannot be found among the listing $q_{1}, q_{2}, ..., q_{s}$, for this would lead to the contradiction that $r_{i} \mid 1$"?

## Calculus, Volume 1, Page 7 Why does n < b^3/(A-b^3/3) lead to contradiction? (Tom M. Apostol 2nd Edition) Paid Members Public

Page 7 on "Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra", why does $n < \frac{b^3}{A - \frac{b^3}{3}}$ lead to contradiction?