Wikipedia:Reference desk/Mathematics: Difference between revisions

 

:The question is unclear. The equation <math>q^2=k^2+1</math> has a solution in <math>q</math> when <math>k=0</math> or <math>k=i.</math> Do you mean, prove that the equation <math>q^2=k^2+1</math> has no general solution in <math>q</math> for ''all'' values of <math>k</math>? Then it is sufficient to give just a single counterexample, like the unsolvability of <math>q^2=2.</math> Or does the use of "real integer" in the question mean that we should understand the variables <math>q</math> and <math>k</math> to range over <math>\Z</math>, and is your question whether the (simple) proof that this has no non-trivial solutions in <math>\Z</math> can be made complicated by involving the Gaussian integers? I have no idea what "equation of 1" means, and what the "it" is that can be decomposed to this equation. If you want us to consider your questions, you should really put more effort in formulating them clearly. &nbsp;--{{#ifeq:{{FULLPAGENAME}}|{{#invoke:Redirect|main|User talk:Lambiam}}|Lambiam|{{#if:Lambiam|[[User talk:Lambiam|Lambiam]]|[[User talk:Lambiam]]}}}} 07:46, 28 February 2021 (UTC)

 

= February 28 =