1. Nov 30, 2008

### disregardthat

I read in a book about Fermats last theorem that it has been proved that "if there are solutions to the equation a^n+b^n=c^n, then there are only a finite number of them". I searched this up and found this article:

http://findarticles.com/p/articles/mi_m1200/is_n12_v133/ai_6519267

A quote from the article states:

How can this be?
Suppose $$a_0, b_0$$ and $$c_0$$ are solutions to the equation $$a^n+b^n=c^n$$ for a specified n, i.e $$a_0^n+b_0^n=c_0^n$$. But by multiplying by $$k^n$$ where k is a natural number larger than 1 yields $$(a_0k)^n+(b_0k)^n=(c_0k)^n$$ which is a different solution. This is true for all values of k larger than 1, so I cannot see how the theorem is true.

2. Nov 30, 2008

### morphism

There's (probably) the unstated assumption that gcd(a,b,c)=1.

3. Nov 30, 2008

### disregardthat

Yes, I thought of that, but I didn't see it anywhere. It is most likely true though.

4. Nov 30, 2008

### Werg22

There are 0 solutions, so it is definitely (not most likely) true!

5. Nov 30, 2008

### disregardthat

Of course =), but before fermats was proven this theorem was probably of importance.