- #1
- 1,218
- 22
What are they? And what does it mean to say that all elliptic curves are modular?
Trying to understand Fermat's Last Theorem.
Trying to understand Fermat's Last Theorem.
What are they? And what does it mean to say that all elliptic curves are modular?
Trying to understand Fermat's Last Theorem.
I know that it proves that for n>2, there is no integer solution to the equation a^n+b^n=c^n. I know that Fermat proved this for n^4 by using "infinite descent". I know that because of this, his theorem is true for all positive composite numbers. Also, I believe that it would be true for all negative numbers as well, that is, the n>2 could be replaced with |n|>2.
Finally, I know that the complete solution involves something about modularity and elliptic curves... which I think have the equation y^2=x^3 or something like that.
That's about it.
I think that if you want us to answer your questions, we need to know what is your mathematical education level...you can also try to read meanwhile Wikipedia
So... does the proof at n=4 prove the theorem for all even numbers greater than 4, maybe?The underlined sentence is false. Fermat's proof of the case n = 4 implies that it suffices to consider odd prime exponents, but not what you typed.
Currently taking AP Calculus BC in high school... also, if something is given to me in understandable terms, i can usually understand it. Usually.
So... does the proof at n=4 prove the theorem for all even numbers greater than 4, maybe?
It's clear. However, my original question was never answered: what are elliptic curves, what is modularity, and why are all elliptic curves modular?