Fermat and His Method of Infinite Descent
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Jamie Bailey, Brian Oberg  
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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