Fermat's Last Theorem

Author

Eric W. Weisstein
January 5, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DiophantineEquations/FermatsLastTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FermatsLastTheorem.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Simpson's Fallacious Counterexample

num={1782^12+1841^12,1922^12}

Position[Equal@@@Transpose[IntegerDigits/@num],False,1,1][[1,1]]-1

"Proof"

FullSimplify[x^n+y^n==z^n,Element[x|y|z|n,Integers]&&n>2&&x y z≠0]

TimeConstrained[Reduce[x^n+y^n==z^n&&Element[x|y|z|n,Integers]&&n>2&&x y z≠0,{x,y,z,n}],3600]//Timing

Reduce[x^n+y^n==z^n&&n>2&&x y z≠0,{x,y,z,n},Integers]

Exists[{x,y,z,n},Element[x|y|z|n,Integers]&&n>2&&x y z≠0,x^n+y^n==z^n]