- #1

musicgold

- 304

- 19

*The art of the infinite:the pleasures of mathematics.*I want to understand how to prove it.

## Homework Statement

Consider a 3-rhythm starting with 2: ## 2, 5, 8, 11, 14, 17...##

The each number in this sequenc has the form ##3n-1##.

The book says that each of these terms can have prime factors of only the following forms: ## 3n-1,~ 3n,~ 3n+1 ...(1)##

Then it claims that no term could have all factors of the form ##3n ~ or 3n+1, ~ or ~ 3n ~ and ~ 3n+1 ...(2)##

Then it claims that each term in the sequence has to have at least one prime factor of the form ##3n-1 ...(3)##

## Homework Equations

## The Attempt at a Solution

While I get claim (2) but I am not clear about how I can prove claims (1) and (3). I have tried manually testing and the claims are correct, however I want to prove them. How should I go about it?