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Beginning of Paper
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By: Jayme
Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that creat ....
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Middle of Paper
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.... number can be expressed as the difference of two square integers in only one way. Fermat's proof is as follows. Let n be prime, and suppose it is equal to x2 -y2 that is, to (x+y)(x-y). Now, by hypothesis, the only basic, integral factors of n and n and unity, hence x+y=n and x-y=1. Solving these equations we get x=1 /2 (n+1) and y=1 /2(n-1). -He gave a proof of the statement made by Diophantus that the sum of the squares of two numbers cannot be the form of 4n-1. He added a corollary which I take to mean that it is impossible that the product of a squar ....
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