Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q1

This is my solution for Chapter 3.2 Q1 in the book Elementary Number Theory 7th Edition written by David M. Burton.

Background

All theorems, corollaries, and definitions listed in the book's order:

Theorems and Corollaries in Elementary Number Theory (Ch 1 - 3)

All theorems and corollaries mentioned in David M. Burton’s Elementary Number Theory are listed by following the book’s order. (7th Edition) (Currently Ch 1 - 3)

RanblogRan

I will only use theorems or facts that are proved before this chapter. So you will not see that I quote theorems or facts from the later chapters.

Question

Determine whether the integer $701$ is prime by testing all primes $p \leq \sqrt{701}$ as possible divisors. Do the same for the integer $1009$.

Solution

For $701$, $p \leq \sqrt{701} \approx 26.48$ means all primes $p \leq 26$.

All primes $\leq 26$ are $2, 3, 5, 7, 11,13, 17, 19,$ and $23$. $701$ is not divisible by any of these. Thus $701$ is prime.

For $1009$, $p \leq \sqrt{1009} \approx 31.76$ means all primes $\leq$ 31.

All primes $\leq 31$ are $2, 3, 5, 7, 11,13, 17, 19, 23, 29$ and $31$. $1009$ is not divisible by any of these. Thus $1009$ is prime.

Read More: All My Solutions for This Book

Related Pages

< Chapter 3.1 Chapter 3.2, Q2 >