# Factorization of rings problem

1. May 30, 2009

### zetafunction

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

in order to factorize 20 on the rings of $$Q( \sqrt 2)$$ i must solve

2. Relevant equations

$$x^{2} -2y^{2}=10$$

3. The attempt at a solution

i do not know how to solve it, i have tried by brute force with calculator but can not get any response , the given hint is that $$x^{2} -2y^{2}=5$$ has no solution.

2. May 30, 2009

### matt grime

Re: factorization

I can only guess that you've factored 20 as 2*10, so why have you not factored 10 as 2*5?

3. May 30, 2009

### zetafunction

Re: factorization

according to the teacher, who put the exercise the diophantine equation

$$x^{2}-2y^{2}=5$$ has no solution on integers.