Beginning of Essay
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. , like many mathematicians of the early 17th century, found solutions to the four major problems t ....

Middle of Essay
.... represent the final form of his research, and therefore cannot be dated earlier than 1660. Mr. 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 ....