Fermat’s last theorem (analytic form of)

Let x, y, z be positive real numbers.

For each positive integer r, let

ar=(xr+yr)/r! and br=zr/r!.

For s divisible by 4, let



Then Fermat’s last theorem is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath (by elementary means) to:

Theorem If an=bn for some odd integer n>2, then either

(i) AN>0 for some N>x,y,


(ii) BM>0 for some M>z.

For a proof that these theorems are equivalent see:

proof of equivalence of Fermat’s Last Theorem to its analytic form

Title Fermat’s last theorem (analytic form of)
Canonical name FermatsLastTheoremanalyticFormOf
Date of creation 2013-03-22 16:17:34
Last modified on 2013-03-22 16:17:34
Owner whm22 (2009)
Last modified by whm22 (2009)
Numerical id 8
Author whm22 (2009)
Entry type Theorem
Classification msc 11D41