1827: French mathematician Sophie Germain saw her theorem, known as Germain's Theorem, published in a footnote of a book by the mathematician Adrien-Marie Legendre. In this theorem Germain proved that if "x", "y", and "z" are integers and if "x" + "y" = "z" then either "x", "y", or "z" must be divisible by 5. Germain's theorem was a major step toward proving Fermat's last theorem for the case where n equals 5.