Yes but what you get when you divide a^7 with a^2 is not coprime to a. So when you set (c-b) = n you can move out of the brackets in (#) another (c-b) part. Since when we prove l is coprime to (c-b) what is left in the brackets is coprime to (c-b) so because of that and triangle inequality, (c-b)^2 divides one whole part of a on the n power, and this never has a solution.I will take now some days off. In summer I will try to prove something else, when I have more time.I am tired of this FLT problem. Have you seen Ramsey the other one? That an odd perfect number does not exist? I have a good intuition sometimes and I was always good in abstract logic, But in Math formulation I am not. I am preety sure the last proof goes this way. There could be some mistakes. It would be the best for me if I could connect with someone who is good at math and when I have an idea, he proves it or not within few minutes.
I know nothing about modularity sorry. All I know is that the equation (3) satisfy the condition. When (c-b) =n it follows that (c-b)^2 divides c^n - b^n OR when (a+b) = n (a+b)^2 divides a^n + b^n alternating binomial factors form (c-b)^(n-1) when transformed to (2) they give rise to equation (3) no doubt about that. Now I will take a break for few days. I have enough of FLT. Ramsey are there any other Math puzzles in Number theory? The ones you dont need complicated mathematical tools to understand them? I mean I would like to start something, which is formulated very simple...Is there any list?
Thanks and we hear in few days.
I claimed that (c-b) is coprime to l. This I havent proved, it arise from the experiences.Thats thats the thing I am asking MATH EXPERTS several times. Is it so hard to prove that (c-b) is coprime to l? I mean when this is not working simply leave it.