Prove the statement ( that values of Mood's test statistic for equality of dispersion test differ by at least one.)

[Darya]

I want to prove that values of Mood's test statistic for equality of dispersion test differ by at least one. This is the statement. I tried to prove it by using multivatiable induction on m,n but no success.. Any ideas?

 

[Darya]

Pardon me, the elements of the first sum also have to be squared

 

[Darya]

All done, thanks!