- #1

Shackleford

- 1,656

- 2

## Homework Statement

Assume that n > 1 is an integer such that p does not divide n for all primes ≤ n

^{1/3}. Show that n is either a prime or the product of two primes. (Hint: assume to the contrary that n contains at least three prime factors. Try to derive a contradiction.)

## Homework Equations

Divisibility, etc.

## The Attempt at a Solution

Assume that there exists three primes such that n = p

_{1}p

_{2}p

_{3}.

I suspect that you need to somehow show that there is a prime less than the cubic root that does divide n, but I'm not sure how to show it.