- #1

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**I**

## Homework Statement

Give that [itex]p\nmid n[/itex] for all primes [itex]p\leq \sqrt[3]n[/itex] show that n> is either prime or the product of two primes.

## Homework Equations

?

## The Attempt at a Solution

I don't really see how to start this one. Any hint would be greatly appreciated

**II.**

## Homework Statement

Give another proof of the infinitude of primes by assuming that there are only finitely many primes say [itex]p_1, p_2, ... p_n[/itex], and using the following integer to arrive at a a contradiciton:

N = [tex]p_2p_3...p_n + p_1p_3...p_n +...+p_1p_2...p_{n-1}[/tex]

## Homework Equations

## The Attempt at a Solution

I think that this proof should involve showing that [itex]p_k\nmid N\forall k[/itex] so N must be prime. Which would be like like Euler proof, but I can't seem to see how to set that up