Pierre De Fermat
Pierre De FermatPierre 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 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 occupation. Mr. 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-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime to n and p(n) 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. 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 square and a prime form 4n-1[even if multiplied by a number that is prime to the latter], can be either a square or the sum of two squares. For example, 44 is a...
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