Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q19

My Solution for "In $1950$, it was proved that any integer $n > 9$ can be written as a sum of distinct odd primes. Express the integers $25$, $69$, $81$, and $125$ in this fashion."

Ran
Ran

Table of Contents


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 question. So you will not see that I quote theorems or facts from the later chapters.

Question

In $1950$, it was proved that any integer $n > 9$ can be written as a sum of distinct odd primes. Express the integers $25$, $69$, $81$, and $125$ in this fashion.

Solution

$25 = 5 + 7 + 13$
$69 = 47 + 17 + 5$
$81 = 47 + 31 + 3$
$125 = 67 + 53 + 5$

Read More: All My Solutions for This Book

< Chapter 3.3, Q18 Chapter 3.3, Q20 >

MathNumber TheorySolution
Ran

Ran

Comments

You might also like

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q10 Members Public

My Solution for "Prove that no integer whose digits add up to $15$ can be a square or a cube. [Hint: For any $a$, $a^{3} \equiv 0$, $1$, or $8$ $\pmod 9$.]"

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q9 Members Public

My Solution for "Find the remainder when $4444^{4444}$ is divided by $9$. [Hint: Observe that $2^{3} \equiv -1 \pmod {9}$.]"

Ran
Ran
Math