# Algebra: show that x > 1 is prime

1. Nov 16, 2009

### Vince00

1. The problem statement, all variables and given/known data
2.4 Show that x > 1 is prime, iff x doesn't have any divisor t; where 1 < t $$\leq \sqrt{x}$$. It is given that x,t $$\in$$ N.

2. Relevant equations
?

3. The attempt at a solution
The "iff" thing makes me think; what can I do to show this?
I have to show that x (x can be 2, 3, 4, 5, 6, ...) is prime if there is no "t", 1<t$$\leq \sqrt{x}$$ (t can be 1, 2, 3, 4, ...) that divides x. AND that that there is no t that divides x if x is prime.
So I have to show it 2 ways.
First: x is prime if t doesn't divide x
Second: t doesn't divide x if x is prime

Vince, fresmen physics.

2. Nov 16, 2009

### tiny-tim

Welcome to PF!

Hi Vince! Welcome to PF!

(have a square-root: √ and a ≤ )

Try starting with the opposite

suppose x is not prime, and all its factors (two or more) are > √x.

3. Nov 21, 2009

### Vince00

Re: Welcome to PF!

Thanks for the welcome tim!
Okay, so you said: suppose x is not prime, and all its factors are > √x

I really have no idea what I can do with that...I tried, for a few days, but I just don't get it!
Maybe you can explain it a bit more?
Tnx!

4. Nov 21, 2009

### tiny-tim

Hi Vince00!

Take 103 and 105 …

how many factors can they have > 10 ?