7th grade FLVS help @freckles

Question

anonymous · Answer

Prove that the equation$$a^n + b^n = c^n$$has no positive integral triples (a, b, c) as solutions for $n \ge 3$ and $n \in \mathbb N$.

imqwerty · Answer

i saw this one 4 days ago :)

parthkohli · Answer

pls tell the proof here

anonymous · Answer

n > 2 it says

anonymous · Answer

There is not enough space to fit it in this text box. :)

imqwerty · Answer

(B FLT is beyond 7th grade scope i ws trynna get a basic solution lol

parthkohli · Answer

^ Hah.

alexandervonhumboldt2 · Answer

i like your username

parthkohli · Answer

ty

alexandervonhumboldt2 · Answer

i wonder why parths dog is so popular

parthkohli · Answer

because that is me.

freckles · Answer

i'm having trouble with just the case n=3

parthkohli · Answer

Ahahaha.

freckles · Answer

I played with some stuff and have
$$a+b=\frac{c^3}{(a+b)^2-3ab} \ \text{ and since } a \text{ and } b \text{ are assumed to be integers } \ \text{ then } a+b \text{ is also }$$
But I don't if there will be at least one case where (a+b)^2-3ab divides c^3 or not.

freckles · Answer

I guess I was looking for a proof by contradiction

parthkohli · Answer

It took three-hundred years to prove this statement ever since it was proposed. Not that easy.

freckles · Answer

oh it has been proved somewhere?

parthkohli · Answer

yes. https://en.wikipedia.org/wiki/Wiles%27_proof_of_Fermat%27s_Last_Theorem

freckles · Answer

He's so fancy.

freckles · Answer

I wish I could be that fancy in math.

parthkohli · Answer

```
Wiles stumbled upon a revelation, "so indescribably beautiful... so simple and so elegant,"
```
I don't find using elliptic curves in number theory elegant. lol

But really, what an achievement it was! Great man.

freckles · Answer

lol

freckles · Answer

i think i will never graduate from elementary number theory.