Among Fermat's various contributions to mathematics, the most prominent one is to lay the foundation of modern number theory. In this field, Fermat has extraordinary intuition and ability. It first attracted Fermat's attention to number theory. Maybe it is the Latin translation of Arithmetic translated by Bachettde Meziriac in 162 1. Many of Fermat's contributions in this field are written in the margin of his manuscript, which was translated by Meziriac in 1670 five years after his death. These notes were compiled by his son Samuel into a new edition of Arithmetic (not carefully printed) and published. Many unproven theorems published by Fermat were later proved to be correct, including Fermat's conjecture (now Fermat's last theorem) which was second only to Goldbach's conjecture at that time.