Timeline for Proving that there are no solutions other than a few known ones

6 events

when toggle format	what		by	license	comment
Oct 31 at 1:22	comment	added	Sam Hopkins		In a sense any classification theorem (e.g. the classification of finite simple groups) is of this form...
S Oct 31 at 1:20	history	suggested	J. W. Tanner		added examples tag
Oct 30 at 22:48	review	Suggested edits
S Oct 31 at 1:20
Oct 30 at 18:52	history	edited	Valerio_xula	CC BY-SA 4.0	corrected typo
Oct 30 at 17:25	comment	added	Joe Silverman		"...any "proof of non-existence" cannot work in full generality because it cannot be valid in those few special cases." For Diophantine equations, it's more precise. Usually the first method one tries is to show that there are no solutions modulo $p$ for one (or a small handful) of primes $p$. For any given $p$, that's a finite task, and if it works, then there are also no integer solutions. But if there is an integer solution, then checking mod $p$ won't rule out integer solutions (it can't). For some equations, solutions mod $p$ for all $p$ (including $p=\infty$) implies an integer solution.
Oct 30 at 16:56	history	asked	Valerio_xula	CC BY-SA 4.0