# Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q7

My Solution for "A conjecture of Lagrange ($1775$) asserts that every odd integer greater than $5$ can be written as a sum $p_{1} + 2p_{2}$, where $p_{1}$, $p_{2}$ are both primes. Confirm this for all odd integers through $75$."

## Table of Contents

Background

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

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

## Question

A conjecture of Lagrange ($1775$) asserts that every odd integer greater than $5$ can be written as a sum $p_{1} + 2p_{2}$, where $p_{1}$, $p_{2}$ are both primes. Confirm this for all odd integers through $75$.

## Solution

(I wrote a program for this question.)

$7 = 3 + 2 \times 2$

$9 = 3 + 2 \times 3$

$11 = 5 + 2 \times 3$

$13 = 3 + 2 \times 5$

$15 = 5 + 2 \times 5$

$17 = 3 + 2 \times 7$

$19 = 5 + 2 \times 7$

$21 = 7 + 2 \times 7$

$23 = 13 + 2 \times 5$

$25 = 3 + 2 \times 11$

$27 = 5 + 2 \times 11$

$29 = 3 + 2 \times 13$

$31 = 5 + 2 \times 13$

$33 = 7 + 2 \times 13$

$35 = 13 + 2 \times 11$

$37 = 3 + 2 \times 17$

$39 = 5 + 2 \times 17$

$41 = 3 + 2 \times 19$

$43 = 5 + 2 \times 19$

$45 = 7 + 2 \times 19$

$47 = 13 + 2 \times 17$

$49 = 3 + 2 \times 23$

$51 = 5 + 2 \times 23$

$53 = 7 + 2 \times 23$

$55 = 17 + 2 \times 19$

$57 = 11 + 2 \times 23$

$59 = 13 + 2 \times 23$

$61 = 3 + 2 \times 29$

$63 = 5 + 2 \times 29$

$65 = 3 + 2 \times 31$

$67 = 5 + 2 \times 31$

$69 = 7 + 2 \times 31$

$71 = 13 + 2 \times 29$

$73 = 11 + 2 \times 31$

$75 = 13 + 2 \times 31$

**Read More:** All My Solutions for This Book

## Related Pages

### Ranblog Newsletter

Join the newsletter to receive the latest updates in your inbox.