# Homework Help: Basis arithmetic problem

1. Jun 12, 2010

### penguin007

1. The problem statement, all variables and given/known data
Hi everyone.
I'm studying a problem and I need to prove that I have a basis. I tryed a proof and to achieve it I need to show that :

if k divides a*b and also divides a2 +2*b2 Then k divides both a and b.

2. Relevant equations

I'm not sure what I'm asserting is true but if it was, then it would be great for me ( cause my proof would be finished).
I first thought that if k divided a sum then it divided every term of that sum but I understood it was wrong (the other way is correct).

I'm taking any idea!

2. Jun 12, 2010

### Tedjn

Re: Arithmetic-question

No, what if a = b and k = a2 in general?

3. Jun 12, 2010

### penguin007

Re: Arithmetic-question

That's right indeed. But what if k is prime??

4. Jun 12, 2010

### Tedjn

Re: Arithmetic-question

If k = 2, then no. Why? If k > 2 is prime, then yes. Why? Use the property that if p is prime and divides ab, then it divides a or b.

5. Jun 13, 2010

### penguin007

Re: Arithmetic-question

I can see if k>2, thank you, but why is it wrong if k=2 ?

6. Jun 13, 2010

### Tedjn

Re: Arithmetic-question

Let a be even and b be odd.