# Pierre De Fermat's Number Theory

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Introduction Pierre de Fermat was born August 17, 1601 in Beaumont-de-Lomagne, France. After pursuing his bachelor in civil law from the University of Toulouse, he spent a great deal of time researching calculus and corresponding with other mathematicians. Fermat was perhaps best known for the “integrity of his commitment to the cause of mathematical truth” [1] and sought to establish himself as a legitimate mathematician aside from his main profession as a lawyer. He was rather political about his work and frequently disputed with René Descartes over matters of credibility and reputation. Fermat was prone to criticism from his contemporaries, who often viewed his problems as trivial. Nevertheless, many of his achievements were invaluable to Newton and Leibniz during the invention of calculus. Throughout the early 17th century, Pierre de Fermat made contributions that were revolutionary in the development of modern arithmetic. Number Theory The method by which Fermat proved several of his theorems was referred to as infinite descent. This states that there is a finite amount of positive integers less than any given positive integer, an idea that led to the proposition famously known as Fermat’s Last Theorem. In modern notation, this contends that if a, b and c are integers greater…show more content…
Fermat states that the sum of the squares of lines AI, EI, and CI, connecting points A, C, and E with point I on the locus, is equal to a given area. He then considers the normals AB, EF, and CD, which are lines perpendicular to the tangent line of the curve at point I. Given the squares of these normals, their difference is equal to the sum of BI2 , FI2 , and DI2 . The lines BI, FI, and DI are said to converge on the same point from locations in the same plane, and thus the sum of their squares is equal to the given area. By correlating … with … , Fermat …