# Generalising fermat's last Theorum **URL:** \ **Category:** Factual Questions\ **Created:** [May 28, 2011, 11:48am UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553 "2011-05-28T11:48:31Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 28, 2011, 11:48am UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/1 "2011-05-28T11:48:31Z")
Do you think it would be possible to expand on Fermat’s Last theorum and generalise a bit more? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 28, 2011, 7:00pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/2 "2011-05-28T19:00:38Z")
It’s certainly possible to generalize on it, in infinitely many ways. How easy it is to prove those generalizations, and how interesting any of them are, are another story. It’s pretty safe to say that there is no interesting generalization that can be proven by an amateur, given how difficult Fermat’s theorem itself was to prove. And there’s no need to start multiple threads or private message people about this. The discussion in the other thread is, or should be, enough. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [May 28, 2011, 7:20pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/3 "2011-05-28T19:20:08Z")
There are two generalizations I am aware of. The first simply says that, known examples aside, the equations x^a + y^b = z^c has no solutions in integers. Known exceptions include that one of the exponents is 1, or that all are 2, or the sole example of successive powers, 1 + 2^3 = 3^2. The second generalization (from which Fermat and most of the cases of the above would follow) has the silly name of the abc conjecture. It roughly says that if a + b = c, then abc cannot consist only of high powers of primes. i could go into detail, but see [http://en.wikipedia.org/wiki/Abc\_conjecture](http://en.wikipedia.org/wiki/Abc_conjecture) for details. Oddly enough, the corresponding claim for a ring of polynomials in one variable has been proved. The proof uses formal differentiation, which is not available for integers. ---
**Author:** ![Svejk\_1](https://avatars.discourse-cdn.com/v4/letter/s/ea666f/32.png) [@Svejk\_1](https://boards.straightdope.com/u/Svejk_1)\ **Post date:** [May 29, 2011, 2:59pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/4 "2011-05-29T14:59:05Z")
TheorEm ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 29, 2011, 5:52pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/5 "2011-05-29T17:52:42Z")
> [@](#): > > There are two generalizations I am aware of. I’m aware of many more generalizations other than those. For instance, one generalization is “There is no solution to a^n + b^n = c^n for a, b, c, and n all integers and n \> 2, and 1 + 1 = 2”. Yeah, this is a boring generalization, but it’s a perfectly valid one. ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 29, 2011, 5:55pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/6 "2011-05-29T17:55:25Z")
What would you have to do to prove a new generilisation formula ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 29, 2011, 8:16pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/7 "2011-05-29T20:16:25Z")
> [@mla1](#): > > What would you have to do to prove a new generilisation formula You would have to find a proof. There’s absolutely no way to predict what that proof would involve–after all, the basis for the proof of FLT wasn’t even possible to state until the 1950s. ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 29, 2011, 9:28pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/8 "2011-05-29T21:28:03Z")
What is the basis of the FLT proof? ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [May 29, 2011, 10:41pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/9 "2011-05-29T22:41:33Z")
The complete proof of FLT was based on properties of [elliptic curves](http://en.wikipedia.org/wiki/Elliptic_curve) which are related to [group theory](http://en.wikipedia.org/wiki/Group_%28mathematics%29) which grew out of [abstract algebra](http://en.wikipedia.org/wiki/Abstract_algebra) and other fields. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [May 29, 2011, 11:07pm UTC](https://boards.straightdope.com/t/generalising-fermats-last-theorum/583553/10 "2011-05-29T23:07:03Z")
> [@ultrafilter](#): > > You would have to find a proof. There’s absolutely no way to predict what that proof would involve–after all, the basis for the proof of FLT wasn’t even possible to state until the 1950s. But after they proved that FTL was possible, what was to stop them from going back in time and proving it in the 1920s? 🆒 :::d+r::::