# Factorization of rings problem

## Homework Statement

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

## Homework Equations

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

## 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.

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matt grime
Homework Helper

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

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

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