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Fermat's Last Theorem for Gaussian Integer Exponents

by John A. Zuehlke

This article originally appeared in:
American Mathematical Monthly
January, 1999

Subject classification(s): Algebra and Number Theory | Number Theory | Famous Problems
Applicable Course(s): 4.3 Number Theory

Andrew Wiles proves that Fermat's Last Theorem is false for integer exponents larger than \(2 \).  Using the Gelfond-Schneider Theorem on transcendental numbers, the author generalizes Wiles' result easily by showing that Fermat's Last Theorem is false for  Gaussian integer exponents that are not real.

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Capsule Course Topic(s):
Number Theory | Diophantine Problems, Fermat's Last Theorem
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