Does Fermat hold in non-standard models? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T02:15:22Z http://mathoverflow.net/feeds/question/39239 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39239/does-fermat-hold-in-non-standard-models Does Fermat hold in non-standard models? Martin Brandenburg 2010-09-18T19:16:20Z 2010-09-18T19:34:29Z <p>Let \$n \geq 3\$ be a natural number and \$PA\$ denote Peano arithmetic. Do we have</p> <p>\$PA \models \forall x,y,z \geq 1 : x^n + y^n \neq z^n\$?</p> <p>In other words, does Fermat's Last Theorem hold also in non-standard models of the natural numbers?</p> <p>If this problem is open, what is its current state of progress?</p>