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Fermat and His Method of Infinite Descent

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Author:Jamie Bailey, Brian Oberg
Description: The basic method of the infinite descent is as follows: Assume one wants to prove no solution exists with a certain property. First, assume a positive integer, x, posseses such a property. Next, deduce that there exists some positive integer y < x which also has the same property. Repeat this argument an infinite number of times, thus infinitely descending through all integers. This contradicts the fact that there must be a smallest positive integer with this property. Therefore, no positive integer exists with the proposed property. Examples and a discussing proving that Fermat's assertion was false.

Levels: College
Languages: English
Math Topics: Number Theory

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