Okay I hope it's okay if I have a couple question. I've been strugelling a bit with this problem set. About a quarter of the questions I just don't seem to see how to start them. Any hints would be greatly appreciated. Thank you kindly(adsbygoogle = window.adsbygoogle || []).push({});

I

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

?

3. The attempt at a solution

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

II.

1. The problem statement, all variables and given/known data

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]

2. Relevant equations

3. 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

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# Homework Help: Number Theory

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