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Factorization of rings problem

  • #1
391
0

Homework Statement



in order to factorize 20 on the rings of [tex] Q( \sqrt 2) [/tex] i must solve

Homework Equations



[tex] x^{2} -2y^{2}=10 [/tex]

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 [tex] x^{2} -2y^{2}=5 [/tex] has no solution.
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
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I can only guess that you've factored 20 as 2*10, so why have you not factored 10 as 2*5?
 
  • #3
391
0


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

[tex] x^{2}-2y^{2}=5 [/tex] has no solution on integers.
 

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