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Word Count: 862
Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages France Mr Fermats 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 created a form of math called calculus Before Sir Isaac Newton was even born Fermat found a method for finding the tangent to a curve He tried different ways in math to improve the system This was his occupationMr Fermat was a good scholar and amused himself by restoring the work of Apollonius on plane loci Mr Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods He had a habit of scribbling notes in the margins of books or in letters rather than publishing them He was modest because he thought if he published his theorems the people would not believe them He did not seem to have the intention to publish his papers It is probable that he revised his notes as the occasion required His published works represent the final form of his research and therefore cannot be dated earlier than 1660 Mr Pierre de Fermat discovered many things in his lifetime Some things that he did include-If p is a prime and a is a prime to p then ap-1-1 is divisible by p that is ap-1-10 mod p The proof of this first given by Euler was known quite well A more general theorem is that a0-n-10 mod n where a is prime to n and pn is the number of integers less than n and prime to it-An odd prime number can be expressed as the difference of two square integers in only one way Fermats proof is as follows Let n be prime and suppose it is equal to x2 -y2 that is to xyx-y Now by hypothesis
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