1. ## Prime factor

Hi everybody.

Well, I can't undersant this problem:

Show that all integers of the form $\displaystyle 4k+3$ has a prime factor of the same form.

Thanks.

2. ## Re: Prime factor

hi Fernando

that means that if we have an integer n such that

n=4*k+3

then n will have a prime factor p such that

p=4*l+3

Stefy

3. ## Re: Prime factor

Hi Stefy! thanks.

OK but, How can I show that?

4. ## Re: Prime factor

Hi

Assume that it's false and then use congruences to get to a contradiction.

5. ## Re: Prime factor

Originally Posted by anonimnystefy
Hi

Assume that it's false and then use congruences to get to a contradiction.
Thanks, but I'm not using congruences yet. :/

6. ## Re: Prime factor

Too bad.It woulda be much easier if you could use easier.

Still, try to assume the statement isn't correct i.e. that all prime factors are of the form 4Śl+1

7. ## Re: Prime factor

Originally Posted by anonimnystefy
Too bad.It woulda be much easier if you could use easier.

Still, try to assume the statement isn't correct i.e. that all prime factors are of the form 4Śl+1
Hi, Ok anyway thanks xD