Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q3
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)
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
Find all pairs of primes $p$ and $q$ satisfying $p - q = 3$.
Solution
If $q = 2$, $p = q +3 = 5$. This is the first pair.
For $q > 2$, we know $q$ is odd and $p = q + 3$ is an even integer. But this is impossible since both $p$ and $q$ are odd integers.
Therefore, $p = 5$ and $q = 2$ is the only pair.
Read More: All My Solutions for This Book