81i:10022
Yalavigi, C. C.
Solvability of Fermat's equation.
Math. Ed. (Siwan) 12 (1978), no. 3, A69--A70.
10B15


-----------------------------------------------------------------------------
----
      References: 0 Reference Citations: 0 Review Citations: 0


-----------------------------------------------------------------------------
----
From the introduction: "It is well known that the title equation appears in
what is usually described as Fermat's last theorem, Fermat's conjecture, or
Fermat's problem, and they imply the following Fermat assertion, viz. (1)
$x^n+y^n=z^n$ (where $n$ is a positive integer $>2$) has no integral
solutions except the trivial ones in which one of the variables is zero.
"Our objective is to associate equation (1) with an extended field of
rational numbers, and show that the extended field has a splitting field for
equation (1). Consequently, Fermat's assertion follows for rational and
Gaussian integers."


-----------------------------------------------------------------------------

2000b:11028
Zuehlke, John A.(1-CLMB)
Fermat's last theorem for Gaussian integer exponents.
Amer. Math. Monthly 106 (1999), no. 1, 49.
11D41


-----------------------------------------------------------------------------
----
      References: 0 Reference Citations: 0 Review Citations: 0


-----------------------------------------------------------------------------
----
In this amusing note the author gives a one-page proof that $x^n+y^n=z^n$
has no solutions in positive integers $x,y,z$ when $n$ is a Gaussian integer
not belonging to Z. The basic tool is the Gel\cprime fond-Schneider theorem
from transcendental number theory.