Hi dear professors. I want to share with you a little formula of arithmetics in order to know the usefulness of this formula and its meaning according to you. This is the formula like in the attached picture: 1+8*E^2≠3*F^2 where E and F can be any integers.

The proof is easy in the article of this link:

https://www.researchgate.net/publication/387410585_A_mathematical_letter_about_a_condition_that_makes_a_Diophantine_equation_have_no_natural_numbers_as_a_solution