A+B=C Conjecture And Fermat’s Last Theorem

That is like a pythagorean theorem, but I don't think a+b=c is the same as a^n+b^n=c^n. Basic algebra shows that you can't transpose exponents through addition. You can through multiplication, but they need to retain the same coefficient. You did create something like a pythagorean theorem, but in things like Heron's Formula, you see how when you multiply the numbers, it becomes different, and stops working. So, I think it's basic algebra to say that those two equations are different, and can't have the same number theory applied to them. Just because of how exponents work.

I also think to derive formulas, you have to do them through observing structures. A math formula is like a sentence. It describes a shape of some kind--which is why we use them in science--so I think the logic of a^n+b^n=c^n where n equals 2 is describing a specific pattern, where we discovered it through looking at a square. What a^3+b^3=c^3 would be, we don't know, but the logic is still valid, but it describes a specific shape. That's all our formulas are doing.