#1**+1 **

*Solve 3^x + 4^x = 5^x*

x = 2 I don't have a formal proof, I just immediately flashed on a 3-4-5 right triangle.

.

Guest Oct 25, 2019

#2**+1 **

well

3^2+4^2 does equal 5^2

So if x =2 it does work

I expect there are other answers too.

Melody Oct 26, 2019

#3**+1 **

No, I checked on WolframAlpha and x=2 is the only possible answer. However, I have no idea as to how to solve it.

ThatOnePerson Oct 27, 2019

#5**+2 **

Anyone familiar with __Fermat’s Last Theorem,__ will instantly note there are no integer or rational number solutions for (x > 2).

The formal solution method is not difficult, and it demonstrates there is __only one solution__ for this equation. https://math.stackexchange.com/questions/61812/proving-that-2-is-the-only-real-solution-of-3x4x-5x/61819

GA

GingerAle Oct 27, 2019

#7**+1 **

GA how do you prove there are no rational solutions using fermat's last theorem? I don't understand

Guest Oct 27, 2019

#8**+2 **

Well, you are not alone in your absence of understanding.

The **Andrew Wiles** and **Wiles-Taylor** proof of ** Fermat’s Last Theorem **is not conveniently accessible to casual post-graduate Ph.D. students. To understand and hold on to

There were still major *bridges* to build to connect these and other proofs to FLT. One notable *bridge* is in ** Ribet’s proof **of the

Because these curves are not elliptic curves, Andrew Wiles realized they weren’t needed for the FLT proof. Using ** Kolyvagin–Flach** approach to adapt the Iwasawa theory, he circumvented the higher-dimensional Abelian selections, while maintaining the integrity of the proof of the

None of the mathematics for these theories is conveniently accessible to lower-level life forms, but I still think it is very cool!.

GA

GingerAle
Oct 28, 2019